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Outer measure

In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of…

Measurability of sets relative to an outer measure, Overview & Outer measures

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Measurability of sets relative to an outer measure

Carathéodory-measurableMathematicianCarathéodoryAreaAxiom of choice
9 related topics

Overview

MathematicalMeasure theoryFunctionSetExtended real numbers
18 related topics

Outer measures

Collection of all subsetsEmpty setSet function
3 related topics

Outer measure and topology

Metric spaceMetric outer measureBorel sets
3 related topics

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Overview

Outer measures

Measurability of sets relative to an outer measure

Outer measure and topology

Construction of outer measures

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Outer measure

Nodes41
Edges40
Triples36
Avg. degree1.95
Density0.04878
Components1

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Outer measure

Top relations

related to Measurability of sets relative to an outer measure · 7
Outer measure → Carathéodory, Carathéodory-measurable, However, In, Informally, Let, One
related to Construction of outer measures · 5
Outer measure → Method, Method II, Munroe, The, There
related to External links · 4
Outer measure → Encyclopedia, Mathematics, MathematicsCaratheodory, Outer
related to Method II · 4
Outer measure → As, For, Suppose, The
related to Definition of a regular outer measure · 3
Outer measure → Formally, Given, There
related to Restriction · 3
Outer measure → Define, Let, One
related to The regular outer measure associated to an outer measure · 3
Outer measure → Every, Given, Then
related to Outer measure and topology · 2
Outer measure → If, Suppose
related to Outer measures · 2
Outer measure → An, Given
related to Pushforward · 2
Outer measure → Given, One

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Important terminology

measure outer displaystyle set subsets mu theory measures subset one isbn definition function sets metric define -measurable given real measurable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Outer measurerelated to Construction of outer measuresThere0.60section
Outer measurerelated to Construction of outer measuresThe0.60section
Outer measurerelated to Construction of outer measuresMunroe0.60section
Outer measurerelated to Construction of outer measuresMethod0.60section
Outer measurerelated to Construction of outer measuresMethod II0.60section
Outer measurerelated to Definition of a regular outer measureGiven0.60section
Outer measurerelated to Definition of a regular outer measureFormally0.60section
Outer measurerelated to Definition of a regular outer measureThere0.60section
Outer measurerelated to External linksOuter0.60section
Outer measurerelated to External linksEncyclopedia0.60section
Outer measurerelated to External linksMathematicsCaratheodory0.60section
Outer measurerelated to External linksMathematics0.60section

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