In mathematics, an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold: * Every Borel set B ⊆ Rn is μ-measurable in the sense of Carathéodory's criterion: for every A ⊆ Rn, * For every set A ⊆ Rn there exists a Borel set B ⊆ Rn such that A ⊆ B and μ(A) = μ(B). Notice that the set A need not be μ-measurable: μ(A) is however well defined as μ is an outer measure.An outer measure satisfying only the first of these two requirements is called a Borel measure, while an outer measure satisfying only the second requirement (with the Borel set B replaced by a measurable set B) is called a regular measure. The Lebesgue outer measure on Rn is an example of a Borel regular measure. It can be proved that a Borel regular measure, although introduced here as an outer measure (only countably subadditive), becomes a full measure (countably additive) if restricted to the Borel sets. (Wikipedia).
Vernier caliper / diameter and length of daily used objects.
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From playlist Fine Measurements
Micrometer/diameter of daily used objects.
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
Micrometer / diameter of daily used objects
What was the diameter? music: https://www.bensound.com/
From playlist Fine Measurements
The Normal Distribution (1 of 3: Introductory definition)
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From playlist The Normal Distribution
Find the reference angle of a angle larger than 2pi
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
More Standard Deviation and Variance
Further explanations and examples of standard deviation and variance
From playlist Unit 1: Descriptive Statistics
How to find the reference angle of an angle larger than 2pi
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Marcin Sabok: Perfect matchings in hyperfinite graphings
Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 16, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au
From playlist Probability and Statistics
Determining values of a variable at a particular percentile in a normal distribution
From playlist Unit 2: Normal Distributions
Does Infinite Cardinal Arithmetic Resemble Number Theory? - Menachem Kojman
Menachem Kojman Ben-Gurion University of the Negev; Member, School of Mathematics February 28, 2011 I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinit
From playlist Mathematics
Measurable equidecompositions – András Máthé – ICM2018
Analysis and Operator Algebras Invited Lecture 8.8 Measurable equidecompositions András Máthé Abstract: The famous Banach–Tarski paradox and Hilbert’s third problem are part of story of paradoxical equidecompositions and invariant finitely additive measures. We review some of the classic
From playlist Analysis & Operator Algebras
Alexander Bufetov: Determinantal point processes - Lecture 2
Abstract: Determinantal point processes arise in a wide range of problems in asymptotic combinatorics, representation theory and mathematical physics, especially the theory of random matrices. While our understanding of determinantal point processes has greatly advanced in the last 20 year
From playlist Probability and Statistics
Radian Measure (Mini Lesson) - Algebra 2
http://www.youtube.com/vinteachesmath This video provides a mini lesson on the concept of radian measure. In particular, this video shows how the unit circle, circumference, and degree measure of an angle can be used to explain the concept of radian measure. This video is appropriate fo
From playlist Trigonometry (old videos)
David Burguet: Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 2
Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We
From playlist Dynamical Systems and Ordinary Differential Equations
Borel-Cantelli Lemmas for Inhomogeneous Diophantine Approximations and beyond by Victor Beresnevich
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
David Sauzin - On the Resurgent WKB Analysis
Iwill report on a work in progress with F. FAUVET(Université de Strasbourg)and R. SCHIAPPA(University ofLisbon)about the WKB formal expansions solutions to the 1D stationary Schrödinger equation with polynomial coefficients. Our emphasis is on the coequational resurgent structure,
From playlist Resurgence in Mathematics and Physics
Universality of Resurgence in Quantization Theories - 13 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
Absolute notions in model theory - M. Dzamonja - Workshop 1 - CEB T1 2018
Mirna Dzamonja (East Anglia) / 30.01.2018 The wonderful theory of stability and ranks developed for many notions in first order model theory implies that many model theoretic constructions are absolute, since they can be expressed in terms of internal properties measurable by the existenc
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Find the reference angle and sketch both angles in standard position
👉 Learn how to find the reference angle of a given angle. The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we determine the quadrant on which the given angle lies and use the reference angle formula for the quadrant
From playlist Find the Reference Angle
Rolf Schneider: Hyperplane tessellations in Euclidean and spherical spaces
Abstract: Random mosaics generated by stationary Poisson hyperplane processes in Euclidean space are a much studied object of Stochastic Geometry, and their typical cells or zero cells belong to the most prominent models of random polytopes. After a brief review, we turn to analogues in sp
From playlist Probability and Statistics