Articles containing proofs | Theorems in calculus | Theorems in measure theory
In mathematical analysis Fubini's theorem is a result that gives conditions under which it is possible to compute a double integral by using an iterated integral, introduced by Guido Fubini in 1907. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. Fubini's theorem implies that two iterated integrals are equal to the corresponding double integral across its integrands. Tonelli's theorem, introduced by Leonida Tonelli in 1909, is similar, but applies to a non-negative measurable function rather than one integrable over their domains. A related theorem is often called Fubini's theorem for infinite series, which states that if is a doubly-indexed sequence of real numbers, and if is absolutely convergent, then Although Fubini's theorem for infinite series is a special case of the more general Fubini's theorem, it is not appropriate to characterize it as a logical consequence of Fubini's theorem. This is because some properties of measures, in particular sub-additivity, are often proved using Fubini's theorem for infinite series. In this case, Fubini's general theorem is a logical consequence of Fubini's theorem for infinite series. (Wikipedia).
This video states Fubini's Theorem and illustrated the theorem graphically. http://mathispower4u.wordpress.com/
From playlist Double Integrals
Fubini Counterexample (full version)
As promised, here is the full version of the previous "Counterexample to Fubini's Theorem" video, which can be found under the following link: https://youtu.be/cIpakZYdWjo Fubini's theorem states that, under certain assumptions, the double integral of f(x,y) dx dy is equal to the double i
From playlist Real Analysis
Fubini's theorem states that, under certain assumptions, the double integral of f(x,y) dx dy is equal to the double integral of f(x,y) dy dx. In this video, I give an example where Fubini's theorem does NOT apply, by explicitly showing that for a specific function, the two integrals are un
From playlist Double and Triple Integrals
Fubini's Theorem (partial integration) -- Calculus III
This lecture is on Calculus III. It follows Part III of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus III
Matrix algebra: determinants | Appendix B2 | Fibonacci Numbers and the Golden Ratio
What is a the determinant of a matrix? Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Fibonacci Numbers and the Golden Ratio
Martin Schweizer: Some stochastic Fubini theorems
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Caristi's fixed point theorem is a fixed point theorem for functions that are controlled by continuous functions but are necessarily continuous themselves. Let a 'Caristi
From playlist Workshop: "Proofs and Computation"
Multivariable Calculus | Changing the order of integration.
We present Fubini's Theorem and give an example of when changing the order of an iterated integral does not give the same result. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus | Multiple Integrals
Cassini's identity | Lecture 7 | Fibonacci Numbers and the Golden Ratio
Derivation of Cassini's identity, which is a relationship between separated Fibonacci numbers. The identity is derived using the Fibonacci Q-matrix and determinants. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pd
From playlist Fibonacci Numbers and the Golden Ratio
Integration trick_ Teorema di Fubini (Fubini's Theorem)_SUB ENG #SoME1
#integrali #Fubini Risoluzione di un integrale definito con ricorso al teorema di Fubini Rif. Biblio: Ritelli D., Spaletta S., Introductory Mathematical Analysis for Quantitative Finance, 2020, CRC Press, Taylor & Francis Group, LLC Con sottotitoli in inglese (with English subtitles) P
From playlist Summer of Math Exposition Youtube Videos
In this video, I give a very clever proof of Clairaut's theorem, which says that if the partial derivatives f_xy and f_yx are continuous at a point, then must be equal. Usually this is proved using difference quotients, but here I give a proof using double integrals. I also give a nice pro
From playlist Partial Derivatives
Carla Farsi: Proper Lie Groupoids and their structures
Talk by Carla Farsi in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 24, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Fubini's Theorem (Measure Theory Part 19)
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.
From playlist Measure Theory
An improper integral representation of the natural logarithm.
We present a nice integral formula for ln(t) using both Fubini's Theorem and Feynman's trick. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqzJpcuD6InKWZXep2L0z1H8 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/m
From playlist Interesting Integrals
Topologies of the zero sets of random real projective hyper-surfaces... - Peter Sarnak
Workshop on Topology: Identifying Order in Complex Systems Topic: Topologies of the zero sets of random real projective hyper-surfaces and of monochromatic waves Speaker: Peter Sarnak Affiliation: IAS and Princeton University Date: April 7, 2018 For more videos, please visit http://video
From playlist Mathematics
The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).
From playlist Physics