Measure theory | Families of sets
In mathematics, a content is a set function that is like a measure, but a content must only be finitely additive, whereas a measure must be countably additive. A content is a real function defined on a collection of subsets such that 1. * 2. * 3. * In many important applications the is chosen to be a Ring of sets or to be at least a Semiring of sets in which case some additional properties can be deduced which are described below. For this reason some authors prefer to define contents only for the case of semirings or even rings. If a content is additionally σ-additive it is called a pre-measure and if furthermore is a σ-algebra, the content is called a measure. Therefore every (real-valued) measure is a content, but not vice versa. Contents give a good notion of integrating bounded functions on a space but can behave badly when integrating unbounded functions, while measures give a good notion of integrating unbounded functions. (Wikipedia).
Measure Theory 1.1 : Definition and Introduction
In this video, I discuss the intuition behind measures, and the definition of a general measure. I also introduce the Lebesgue Measure, without proving that it is indeed a measure. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
Measure Theory - Part 3 - What is a measure?
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From playlist Measure Theory
(PP 6.1) Multivariate Gaussian - definition
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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
Percentiles, Deciles, Quartiles
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From playlist Unit 1: Descriptive Statistics
In this video, the Flipping Physics team discusses the concept of mass and density by comparing the mass and density of steel and wood. The team first addresses the misconception that steel is always more massive than wood, explaining that the mass of an object cannot be determined without
From playlist Fluids
Joe Neeman: Gaussian isoperimetry and related topics III
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
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From playlist Gravitation: Orbital Velocity, Orbital Period, Potential Energy, Kinetic Energy, Mass and Weight
01.3 - ISE2021 - How to measure information
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 1: Information, Natural Language, and the Web 01.3 - How to measure Information - Information according to Information Theory - Random variables and probability mass
From playlist ISE 2021 - Lecture 01, 14.04.2021
Shannon Nyquist Sampling Theorem
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From playlist Sparsity and Compression [Data-Driven Science and Engineering]
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From playlist Unit 1: Descriptive Statistics
Learning To See [Part 15: Information]
In this series, we'll explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. It's gonna be crazy. Supporting Code: https://github.com/stephencwe
From playlist Learning To See
SHM - 16/01/15 - Constructivismes en mathématiques - Henri Lombardi
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From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
Probability & Information Theory — Subject 5 of Machine Learning Foundations
#MLFoundations #Probability #MachineLearning Welcome to my course on Probability and Information Theory, which is part of my broader "Machine Learning Foundations" curriculum. This video is an orientation to the curriculum. There are eight subjects covered comprehensively in the ML Found
From playlist Probability for Machine Learning
(IC 1.6) A different notion of "information"
An informal discussion of the distinctions between our everyday usage of the word "information" and the information-theoretic notion of "information". A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F Attribution for image of TV static:
From playlist Information theory and Coding
Thibault Damour - Relativité Générale et Trous Noirs : un siècle de développements
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From playlist Évenements grand public
Anil Seth on a New Science of Consciousness | Closer To Truth Chats
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From playlist Closer To Truth Chats
Computational Advances in Social Science Experiments
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From playlist SICSS 2022
More Standard Deviation and Variance
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Bathroom Quantum Fields and Vacuum Energy
Building a bathroom got me all philosophical. Video contents: 0:00 Intro on Bathroom energy 1:51 About energy conservation 3:38 Wave character of particles/matter 5:06 Concept and value of vacuum energy 11:08 When theory takes a silly turn 12:25 About probability in QM 16:09 What is a meas
From playlist optics