In mathematics, the support (sometimes topological support or spectrum) of a measureμ on a measurabletopological space (X,Borel(X)) is a precise notion of where in the space X the measure "lives". It is defined to be the largest (closed) subset of X for which every openneighbourhood of every point of the set has positive measure.
Motivation
A (non-negative) measure μ on a measurable space (X,Σ) is really a function μ:Σ→[0,+∞]. Therefore, in terms of the usual definition of support, the support of μ is a subset of the σ-algebra Σ:
where the overbar denotes set closure. However, this definition is somewhat unsatisfactory: we use the notion of closure, but we do not even have a topology on Σ! What we really want to know is where in the space X the measure μ is non-zero. Consider two examples:
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space Rn. For instance, the Lebesgue measure of the interval[0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1.
Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (seeDefinition below). It must assign 0 to the empty set and be (countably) additive: the measure of a 'large' subset that can be decomposed into a finite (or countable) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. Indeed, their existence is a non-trivial consequence of the axiom of choice.
In technical analysis, support and resistance is a concept that the movement of the price of a security will tend to stop and reverse at certain predetermined price levels. These levels are denoted by multiple touches of price without a breakthrough of the level.
Support versus resistance
A support level is a level where the price tends to find support as it falls. This means the price is more likely to "bounce" off this level rather than break through it. However, once the price has breached this level, by an amount exceeding some noise, it is likely to continue falling until meeting another support level.
A resistance level is the opposite of a support level. It is where the price tends to find resistance as it rises. This means the price is more likely to "bounce" off this level rather than break through it. However, once the price has breached this level, by an amount exceeding some noise, it is likely to continue rising until meeting another resistance level.
In mathematics, the support of a function is the set of points where the function is not zero-valued or, in the case of functions defined on a topological space, the closure of that set. This concept is used very widely in mathematical analysis. In the form of functions with support that is bounded, it also plays a major part in various types of mathematical duality theories.
Formulation
Suppose that f: X→R is a real-valued function whose domain is an arbitrary set X. The set-theoretic support of f, written supp(f), is the set of points in X where f is non-zero
The support of f is the smallest subset of X with the property that f is zero on the subset's complement, meaning that the non-zero values of f "live" on supp(f). If f(x)=0 for all but a finite number of points xinX, then f is said to have finite support.
If the set X has an additional structure (for example, a topology), then the support of f is defined in an analogous way as the smallest subset of X of an appropriate type such that f vanishes in an appropriate sense on its complement. The notion of support also extends in a natural way to functions taking values in more general sets than R and to other objects, such as measures or distributions.
Theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might for example include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings. A theory is not the same as a hypothesis. A theory provides an explanatory framework for some observation, and from the assumptions of the explanation follows a number of possible hypotheses that can be tested in order to provide support for, or challenge, the theory.
A theory can be normative (or prescriptive), meaning a postulation about what ought to be. It provides "goals, norms, and standards". A theory can be a body of knowledge, which may or may not be associated with particular explanatory models. To theorize is to develop this body of knowledge.
As already in Aristotle's definitions, theory is very often contrasted to "practice" (from Greek praxis, πρᾶξις) a Greek term for "doing", which is opposed to theory because pure theory involves no doing apart from itself. A classical example of the distinction between "theoretical" and "practical" uses the discipline of medicine: medical theory involves trying to understand the causes and nature of health and sickness, while the practical side of medicine is trying to make people healthy. These two things are related but can be independent, because it is possible to research health and sickness without curing specific patients, and it is possible to cure a patient without knowing how the cure worked.
The game of chess is commonly divided into three phases: the opening, middlegame, and endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often but not necessarily also eminent players, are referred to as "theorists" or "theoreticians".
"Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles.
The development of theory in all of these areas has been assisted by the vast literature on the game. In 1913, preeminent chess historian H. J. R. Murray wrote in his 900-page magnum opus A History of Chess
that, "The game possesses a literature which in contents probably exceeds that of all other games combined." He estimated that at that time the "total number of books on chess, chess magazines, and newspapers devoting space regularly to the game probably exceeds 5,000". In 1949, B. H. Wood opined that the number had increased to about 20,000.David Hooper and Kenneth Whyld wrote in 1992 that, "Since then there has been a steady increase year by year of the number of new chess publications. No one knows how many have been printed..." The world's largest chess library, the John G. White Collection at the Cleveland Public Library, contains over 32,000 chess books and serials, including over 6,000 bound volumes of chess periodicals. Chess players today also avail themselves of computer-based sources of information.
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
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published: 12 Jun 2019
Measure Theory 20 | Outer measures - Part 1
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published: 19 May 2020
Measure Theory 6 | Lebesgue Integral
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published: 29 Sep 2019
Measure Theory - Part 17 - Product measure and Cavalieri's principle
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published: 10 Feb 2020
Measure Theory - Part 2 - Borel Sigma Algebras
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published: 16 Jul 2019
Fubini's Theorem (Measure Theory Part 19)
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published: 09 Mar 2020
Measure Theory 3 | What is a measure?
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
Here, I explain the introduction to measure theory, namely sigma algebras.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
00:00 Introduction
02:55 Example
03:51 Definition sigma algebra
09:44 Definition measurable sets
10:18 Example
I hope that this helps students, pupils and others.
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
Here, I explain the introduction to measure theory, namely sigma algebras.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
00:00 Introduction
02:55 Example
03:51 Definition sigma algebra
09:44 Definition measurable sets
10:18 Example
I hope that this helps students, pupils and others.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
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This is part 20 of 22 videos.
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
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This is part 20 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start
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This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 6 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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And a big thank you for everyone who contributes to the subtitles here: https://github.com/thebrightsideofmathematics/bsom-subtitles/tree/main/mt
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 6 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
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Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
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Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/lVO40DJ48pE
There is also a bright mode version of this video: https://youtu.be/BTU69ezkpZw
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
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Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/JWtzasf_Uy4
There is also a bright mode version of this video: https://youtu.be/z5m6HXKx0Wo
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Calculus
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/JWtzasf_Uy4
There is also a bright mode version of this video: https://youtu.be/z5m6HXKx0Wo
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Calculus
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com...
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://thebrightsideofmathematics.com/measure_theory/overview/
To find the YouTube-Playlist, click here: https://youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
This video is about a topic in measure theory, namely the famous Fubini's theorem. Here, I show you some practical example and calculate an integral.
I hope that this helps students, pupils and others.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
New link: https://thebrightsideofmathematics.com/measure_theory/overview/
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://thebrightsideofmathematics.com/measure_theory/overview/
To find the YouTube-Playlist, click here: https://youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
This video is about a topic in measure theory, namely the famous Fubini's theorem. Here, I show you some practical example and calculate an integral.
I hope that this helps students, pupils and others.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
New link: https://thebrightsideofmathematics.com/measure_theory/overview/
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com...
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/GHdBo2uKfiM
There is also a bright mode version of this video: https://youtu.be/7O7qPrNIt7w
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/GHdBo2uKfiM
There is also a bright mode version of this video: https://youtu.be/7O7qPrNIt7w
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://thebrightsideofmathematics.com/measure_theory/overview/
To find the YouTube-Playlist, click here: https://youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
Here, I explain the introduction to measure theory, namely sigma algebras.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
00:00 Introduction
02:55 Example
03:51 Definition sigma algebra
09:44 Definition measurable sets
10:18 Example
I hope that this helps students, pupils and others.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
New link: https://thebrightsideofmathematics.com/measure_theory/overview/
Find more here: https://tbsom.de/s/mt
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or join the channel here: https://www.youtube.com/channel/UCdwo4k1RQHTcq_-WS7Cazqg/join
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/gx1oqVXxhrc
There is also a bright mode version of this video: https://youtu.be/LC-9KzxVoWI
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
And a big thank you for everyone who contributes to the subtitles here: https://github.com/thebrightsideofmathematics/bsom-subtitles/tree/main/mt
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 20 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start
Find more here: https://tbsom.de/s/mt
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or join the channel here: https://www.youtube.com/channel/UCdwo4k1RQHTcq_-WS7Cazqg/join
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/f4FqnwEgR98
There is also a bright mode version of this video: https://youtu.be/TG67nsccqeQ
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
And a big thank you for everyone who contributes to the subtitles here: https://github.com/thebrightsideofmathematics/bsom-subtitles/tree/main/mt
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it. We discuss sigma algebra, measures, and integration. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
#Probability
This is part 6 of 22 videos.
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
The Bright Side of Mathematics has whole video courses about different topics and you can find them here https://tbsom.de/s/start
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/lVO40DJ48pE
There is also a bright mode version of this video: https://youtu.be/BTU69ezkpZw
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/JWtzasf_Uy4
There is also a bright mode version of this video: https://youtu.be/z5m6HXKx0Wo
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Calculus
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://thebrightsideofmathematics.com/measure_theory/overview/
To find the YouTube-Playlist, click here: https://youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
This video is about a topic in measure theory, namely the famous Fubini's theorem. Here, I show you some practical example and calculate an integral.
I hope that this helps students, pupils and others.
#MeasureTheory
Spanish subtitles by Jorge Ibáñez. Thank you :)
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
New link: https://thebrightsideofmathematics.com/measure_theory/overview/
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths
Or support me via PayPal: https://paypal.me/brightmaths
Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics
Or via Patreon: https://www.patreon.com/bsom
Or via other methods: https://thebrightsideofmathematics.com/support/
Watch the whole video series about Measure Theory and download PDF versions and quizzes: https://tbsom.de/s/mt
There is also a dark mode version of this video: https://youtu.be/GHdBo2uKfiM
There is also a bright mode version of this video: https://youtu.be/7O7qPrNIt7w
To find the YouTube-Playlist, click here for the bright version: https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j
And click here for the dark version of the playlist: https://www.youtube.com/playlist?list=PLBh2i93oe2quIJS-j1NpbzEvQCmN00F5o
Thanks to all supporters! They are mentioned in the credits of the video :)
Spanish subtitles by Jorge Ibáñez. Thank you :)
This is my video series about Measure Theory. I hope that it will help everyone who wants to learn about it.
#MeasureTheory
#Analysis
#Integral
#Calculus
#Measures
#Mathematics
x
(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
In mathematics, the support (sometimes topological support or spectrum) of a measureμ on a measurabletopological space (X,Borel(X)) is a precise notion of where in the space X the measure "lives". It is defined to be the largest (closed) subset of X for which every openneighbourhood of every point of the set has positive measure.
Motivation
A (non-negative) measure μ on a measurable space (X,Σ) is really a function μ:Σ→[0,+∞]. Therefore, in terms of the usual definition of support, the support of μ is a subset of the σ-algebra Σ:
where the overbar denotes set closure. However, this definition is somewhat unsatisfactory: we use the notion of closure, but we do not even have a topology on Σ! What we really want to know is where in the space X the measure μ is non-zero. Consider two examples: