Covering lemmas | Theorems in analysis
In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover. The Besicovitch covering theorem asserts that there exists a constant cN depending only on the dimension N with the following property: * Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1 = {Bn1}, …, AcN = {BncN} contained in F such that each collection Ai consists of disjoint balls, and Let G denote the subcollection of F consisting of all balls from the cN disjoint families A1,...,AcN.The less precise following statement is clearly true: every point x ∈ RN belongs to at most cN different balls from the subcollection G, and G remains a cover for E (every point y ∈ E belongs to at least one ball from the subcollection G). This property gives actually an equivalent form for the theorem (except for the value of the constant). * There exists a constant bN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there is a subcollection G of F such that G is a cover of the set E and every point x ∈ E belongs to at most bN different balls from the subcover G. In other words, the function SG equal to the sum of the indicator functions of the balls in G is larger than 1E and bounded on RN by the constant bN, (Wikipedia).
S.Rigot - Besicovitch covering property in sub-Riemannian geometry
The Besicovitch covering property originates from works of Besicovitch about differentiation of measures in Euclidean spaces. It can more generally be used as a usefull tool to deduce global properties of a metric space from local ones. We will discuss in this talk the validity or non vali
From playlist Journées Sous-Riemanniennes 2017
Functional Analysis Lecture 26 2014 05 01 Closed Graph Theorem, Besicovitch Sets
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From playlist Course 9: Basic Functional and Harmonic Analysis
Functional Analysis Lecture 27 2014 05 06 Besicovitch sets are generic
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From playlist Course 9: Basic Functional and Harmonic Analysis
Universal covering spaces | Algebraic Topology | NJ Wildberger
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From playlist Algebraic Topology
Analytic Geometry Over F_1 - Vladimir Berkovich
Vladimir Berkovich Weizmann Institute of Science March 10, 2011 I'll talk on work in progress on algebraic and analytic geometry over the field of one element F_1. This work originates in non-Archimedean analytic geometry as a result of a search for appropriate framework for so called skel
From playlist Mathematics
A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally bi-continuos. The infinite spiral is for example a covering of the circle. Notice how every path on the circle can be lifted to the spiral. If a coveri
From playlist Algebraic Topology
The Tempered Topology (on Berkovich Spaces)
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From playlist Geometry of Frobenioids
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From playlist Summer of Math Exposition Youtube Videos
T. Toro - Geometry of measures and applications (Part 3)
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
T. Toro - Geometry of measures and applications (Part 5)
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
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From playlist Mathematics
T. Toro - Geometry of measures and applications (Part 1)
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
T. Toro - Geometry of measures and applications (Part 2)
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
T. Toro - Geometry of measures and applications (Part 4)
In the 1920's Besicovitch studied linearly measurable sets in the plane, that is sets with locally finite "length". The basic question he addressed was whether the infinitesimal properties of the "length" of a set E in the plane yield geometric information on E itself. This simple question
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
Introduction to Number Theory, Part 5: Bezout's Theorem
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From playlist Introduction to Number Theory
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From playlist Fields Medallists on Numberphile
Algebraic Topology 1.5 : Covering Maps and the Fundamental Group of the Circle
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From playlist Topology