Measure theory | Additive functions
In mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely-additive set function (the terms are equivalent). However, a finitely-additive set function might not have the additivity property for a union of an infinite number of sets. A σ-additive set function is a function that has the additivity property even for countably infinite many sets, that is, Additivity and sigma-additivity are particularly important properties of measures. They are abstractions of how intuitive properties of size (length, area, volume) of a set sum when considering multiple objects. Additivity is a weaker condition than σ-additivity; that is, σ-additivity implies additivity. The term is equivalent to additive set function; see modularity below. (Wikipedia).
Measure Theory 1.2 : Sigma Algebras and the Borel Sigma Algebra
In this video, I introduce sigma algebras, generating sigma algebras, the Borel sigma algebra, and much more. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
(PP 1.2) Measure theory: Sigma-algebras
Definition of a sigma-algebra. 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 interested in the rigorous underpinnings. If you choose to do this, you
From playlist Probability Theory
(PP 1.S) Measure theory: Summary
A brief summary of the material from this section, emphasizing probability measures.
From playlist Probability Theory
(PP 1.3) Measure theory: Measures
(0:00) Sigma-algebra generated by a collection. (4:12) Examples of sigma-algebras. (7:20) Definition of a measure. (9:48) Definition of a probability measure. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB
From playlist Probability Theory
Calculus - Find the limit of a function using epsilon and delta
This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. This particular video uses a linear function to highlight the process and make it easier to understand. Later videos take care of more complicated functions and using epsilon and delta
From playlist Calculus
Mean and Variance of Normal Distribution
Calculus/Probability: We calculate the mean and variance for normal distributions. We also verify the probability density function property using the assumption that the improper integral of exp(-x^2) over the real line equals sqrt(pi).
From playlist Probability
EXTRA MATH 6D: MAximum likelihood estimation for the normal model
Forelæsning med Per B. Brockhoff. Kapitler:
From playlist DTU: Introduction to Statistics | CosmoLearning.org
Using sigma sum notation to evaluate the partial sum
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is
From playlist Series
what is sigma notation and how to we use it
👉 Learn how to find the partial sum of an arithmetic series. A series is the sum of the terms of a sequence. An arithmetic series is the sum of the terms of an arithmetic sequence. The formula for the sum of n terms of an arithmetic sequence is given by Sn = n/2 [2a + (n - 1)d], where a is
From playlist Series
What is a Manifold? Lesson 9: The Tangent Space-Definition
What is a Manifold? Lesson 9: The Tangent Space-Definition This lesson is longer than the others because it is rather technical. I made a slip up at about minute 56 which is annotated in the video and mentioned in the first comment.
From playlist What is a Manifold?
We work over the field \mathbf{C}(x) equipped with the derivation d/dx and the shift operator s with s(f(x))=f(x+1). The difference Galois group of a differential equation over \mathbf{C}(x) measures the algebraic relations among the solutions and its transforms under s and higher powers
From playlist DART X
The Green - Tao Theorem (Lecture 8) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
zkSNARKs -- Recent progress and applications to blockchain protocols by Chaya Ganesh
DISCUSSION MEETING : FOUNDATIONAL ASPECTS OF BLOCKCHAIN TECHNOLOGY ORGANIZERS : Pandu Rangan Chandrasekaran DATE : 15 to 17 January 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore Blockchain technology is among one of the most influential disruptive technologies of the current decade.
From playlist Foundational Aspects of Blockchain Technology 2020
A Practical Introduction to Interpretations.
We give a definition that is necessary for the construction of Hodge Theaters.
From playlist Model Theory
Elliptic Curves - Lecture 9b - The (Picard) group law
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Triangulated persistence categories - Jun Zhang
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Triangulated persistence categories Speaker: Jun Zhang Affiliation: Université de Montréal Date: September 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
2 Ruediger - Stochastic Integration & SDEs
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
20 Tutorial by Ruediger - Stochastic Integration & SDEs
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Ex: Sigma Notation - Summation Involving a Quadratic
This video provides a basic example of how to evaluate a summation given in sigma notation. Site: http://mathispower4u.com
From playlist Series (Algebra)
Omar Fawzi: "New quantum Rényi divergences and applications"
Entropy Inequalities, Quantum Information and Quantum Physics 2021 "New quantum Rényi divergences and applications" Omar Fawzi - École Normale Supérieure de Lyon Abstract: I will discuss new quantum Rényi divergences defined via a convex optimization program and their applications to qua
From playlist Entropy Inequalities, Quantum Information and Quantum Physics 2021