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
Measure Theory 2.2 : Lebesgue Measure of the Intervals
In this video, I prove that the Lebesgue measure of [a, b] is equal to the Lebesgue measure of (a, b) is equal to b - a. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
Measure Theory 2.3 : Open and Closed Inervals are Lebesgue Measurable
In this video, I prove that the open and closed intervals (a, b) and [a, b] (as well as [a, b) and (a, b]) are in fact Lebesgue measurable, and thus validating the previous video in this series. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
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
Measure Theory 3.3 : Riemann Integral Equals Lebesgue Integral
In this video, I describe a new way of defining the Riemann Integral, and use that to prove that the Riemann and Lebesgue Integrals are the same for Riemann Integrable functions. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
Measure Theory 3.1 : Lebesgue Integral
In this video, I define the Lebesgue Integral, and give an intuition for such a definition. I also introduce indicator functions, simple functions, and measurable functions.
From playlist Measure Theory
Measure Theory 3.4: Monotone Convergence Theorem
In this video, I will be proving the Monotone Convergence Theorem for Lebesgue Integrals. Email : fematikaqna@gmail.com Subreddit : https://www.reddit.com/r/fematika Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
(PP 1.5) Measure theory: Basic Properties of Measures
(0:00) Lebesgue measure. (4:33) Basic Properties of Measures: Monotonicity, Subadditivity. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4 You can skip the measure theory (Section 1) if you're not intereste
From playlist Probability Theory
Observable events" and "typical trajectories" in...dynamical systems - Lai-Sang Young
Analysis Seminar Topic: Observable events" and "typical trajectories" in finite and infinite dimensional dynamical systems Speaker: Lai-Sang Young Affiliation: New York University; Distinguished Visiting Professor, School of Mathematics and Natural Sciences Date: February 24, 2020 For mo
From playlist Mathematics
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
GPDE Workshop - External doubly stochastic measures and optimal transportation
Robert McCann University of Toronto February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
60 years of dynamics and number expansions - 10 December 2018
http://crm.sns.it/event/441/ 60 years of dynamics and number expansions Partially supported by Delft University of Technology, by Utrecht University and the University of Pisa It has been a little over sixty years since A. Renyi published his famous article on the dynamics of number expa
From playlist Centro di Ricerca Matematica Ennio De Giorgi
(PP 5.3) Multiple random variables with densities
(0:00) Integral notation. (4:23) Definition of a random vector with a density. (9:00) Marginal PDF, Conditional PMF, and Conditional expectation for random vectors with densities. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567
From playlist Probability Theory
How the Axiom of Choice Gives Sizeless Sets | Infinite Series
Viewers like you help make PBS (Thank you đ) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Does every set - or collection of numbers - have a size: a length or a width? In other words, is it possible for a set to be sizeless? This in an updated version of our
From playlist An Infinite Playlist
V. Franceschi - Sub-riemannian soap bubbles
The aim of this seminar is to present some results about minimal bubble clusters in some sub-Riemannian spaces. This amounts to finding the best configuration of m â N regions in a manifold enclosing given volumes, in order to minimize their total perimeter. In a n-dimensional sub-Riemanni
From playlist Journées Sous-Riemanniennes 2018
Dynamical systems, fractals and diophantine approximations â Carlos Gustavo Moreira â ICM2018
Plenary Lecture 6 Dynamical systems, fractal geometry and diophantine approximations Carlos Gustavo Moreira Abstract: We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related
From playlist Plenary Lectures
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - D.Voiculescu
Dan Voiculescu (UC Berkeley) / 15.09.17 Title: The Macaev operator norm, entropy and supramenability. Abstract: On the (p,1) Lorentz scale of normed ideals of compact operators, the Macaev ideal is the end at infinity. From a perturbation point of view the Macaev ideal is related to ent
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Adaptive schemes for MCMC in infinite dimensions by Sreekar Vadlamani
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Lai-Sang Young: A mathematical Theory of Strange Attractors
This lecture was held at The University of Oslo, May 24, 2006 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2006 1. âA Scandinavian Chapter in Analysisâ by Lennart Carleson, Kungliga Tekniska Högskolan, Swed
From playlist Abel Lectures
In this video, I show how to calculate the integral of x^3 from 0 to 1 but using the Lebesgue integral instead of the Riemann integral. My hope is to show you that they indeed produce the same answer, and that in fact Riemann integrable functions are also Lebesgue integrable. Enjoy!
From playlist Real Analysis