Articles containing proofs | Theorems in measure theory | Real analysis | Inequalities | Lemmas in analysis

Fatou's lemma

In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou. Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated convergence theorem. (Wikipedia).

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Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

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Regularity lemma and its applications Part I - Fan Wei

Computer Science/Discrete Mathematics Seminar II Topic: Regularity lemma and its applications Part I Speaker: Fan Wei Affiliation: Member, School of Mathematics Dater: December 3, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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Measure Theory - Part 9 - Fatou's Lemma [dark version]

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From playlist Measure Theory [dark version]

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Measure Theory - Part 9 - Fatou's Lemma

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

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Maßtheorie - Teil 9 - Lemma von Fatou

Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete Hier erzähle ich etwas über die Maßtheorie. Hier geht es um das Lemma von Fatou und den Beweis von diesem. (Aufgabe passt zur Vor

From playlist Maßtheorie und Integrationstheorie

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Berge's lemma, an animated proof

Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should

From playlist Summer of Math Exposition Youtube Videos

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Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

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Dynamics of polynomial shift-like maps by Sayani Bera

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

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Non-autonomous basins of attraction by Kaushal Verma

Program : Integrable? ?systems? ?in? ?Mathematics,? ?Condensed? ?Matter? ?and? ?Statistical? ?Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Lebesgue Integral Overview

In this video, I present an overview (without proofs) of the Lebesgue integral, which is a more general way of integrating a function. If you'd like to see proods of the statements, I recommend you look at fematika's channel, where he gives a more detailed look of the Lebesgue integral. In

From playlist Real Analysis

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Water and Wine

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Problems, Paradoxes, and Sophisms

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Measure Theory 2.1 : Lebesgue Outer Measure

In this video, I introduce the Lebesgue outer measure, and prove that it is, in fact, an outer measure. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Measure Theory

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John Hamal Hubbard

John Hamal Hubbard: Interview at Cirm Interview date: 24/09/2021 at Cirm Realization/Interview/Post production: Stéphanie Vareilles Camera operator: Guillaume Hennenfent ----------------- Questions/Chapters: 1. John Hubbard can you first describe your research areas? 00:19 2. Why do you

From playlist English interviews - Interviews en anglais

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Sum of Polynomial Coefficients Challenge

Solution on Lemma: https://www.lem.ma/-K (and additional challenges) Tangentially related good read: http://bit.ly/PascalsTri Twitter: https://twitter.com/PavelGrinfeld

From playlist Problems, Paradoxes, and Sophisms

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Riemann-Lebesgue Lemma

In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral

From playlist Real Analysis

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Functional Analysis Lecture 01 2014 01 21 Banach Spaces; L^p spaces

Review: Bounded Convergence Theorem, Fatou's Lemma, Monotone Convergence Theorem, Dominated Convergence Theorem, Radon-Nikodym theorem. Banach spaces: normed vector space; metric; L^p spaces; Holder's inequality; conjugate exponent.

From playlist Course 9: Basic Functional and Harmonic Analysis

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Holly Krieger, Equidistribution and unlikely intersections in arithmetic dynamics

VaNTAGe seminar on May 26, 2020. License: CC-BY-NC-SA. Closed captions provided by Marley Young.

From playlist Arithmetic dynamics

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Universality of Resurgence in Quantization Theories - 15 June 2018

http://crm.sns.it/event/433 Universality of Resurgence in Quantization Theories Recent mathematical progress in the modern theory of resurgent asymptotic analysis (using trans-series and alien calculus) has recently begun to be applied systematically to many current problems of interest,

From playlist Centro di Ricerca Matematica Ennio De Giorgi

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Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=W2pw1JWc9k4&list=PLUl4u3cNGP63micsJp_

From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021

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The Straw Trick

This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt

From playlist Problems, Paradoxes, and Sophisms

Related pages

Lebesgue measure | Zero function | Almost surely | Extended real number line | Convergence of measures | Indicator function | Almost everywhere | Probability space | Disjoint sets | Unit interval | Simple function | Lebesgue integration | Sequence | Lemma (mathematics) | Pointwise | Monotone convergence theorem | Fatou–Lebesgue theorem | Natural number | Mathematics | Function (mathematics) | Null set | Real number | Convergence in measure | Expected value | Σ-algebra | Probability theory | Dominated convergence theorem | Inequality (mathematics) | Measure (mathematics) | Pointwise convergence | Conditional expectation | Uniform convergence