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Measurable function

In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in direct analogy to the definition that a continuous function between topological spaces preserves the topological…

Art, Properties of measurable functions & Overview

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Overview

Formal definition

Term usage variations

Notable classes of measurable functions

Properties of measurable functions

Non-measurable functions

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Map overview Semantic statistics

Measurable function

Nodes39
Edges38
Triples50
Avg. degree1.95
Density0.051282
Components1

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Measurable function

Top relations

related to Notable classes of measurable functions · 11
Measurable function → Borel, Continuous, However, If, In, Lebesgue, Luzin's, Random, Riemann-integrable, Sigma, This
related to Non-measurable functions · 8
Measurable function → Borel, Fraenkel, In, Real-valued, Sigma, Such, This, Zermelo
related to Properties of measurable functions · 8
Measurable function → Borel, If, Indeed, Lebesgue-measurable, Sigma, So, The, This
see also · 7
Measurable function → Banach, Bochner, Function, Generalization, Subject, Type, Vector
related to Term usage variations · 6
Measurable function → Bochner, Borel, For, If, Some, The
related to External links · 4
Measurable function → Encyclopedia, Mathematics, MathematicsBorel, Measurable
related to Formal definition · 4
Measurable function → If, Let, Sigma, That
is a · 2
Measurable function → function between the underlying sets of two measurable spaces that preserves the structure of the spaces, measurable function f

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Important terminology

measurable displaystyle functions function sigma borel spaces mathbb set preimage definition continuous lebesgue space theory non-measurable algebra sets preserves mathrm

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Measurable functionis afunction between the underlying sets of two measurable spaces that preserves the structure of the spaces0.90text
Measurable functionis ameasurable function f0.90text
Measurable functionrelated to External linksMeasurable0.60section
Measurable functionrelated to External linksEncyclopedia0.60section
Measurable functionrelated to External linksMathematicsBorel0.60section
Measurable functionrelated to External linksMathematics0.60section
Measurable functionrelated to Formal definitionLet0.60section
Measurable functionrelated to Formal definitionSigma0.60section
Measurable functionrelated to Formal definitionThat0.60section
Measurable functionrelated to Formal definitionIf0.60section
Measurable functionrelated to Non-measurable functionsReal-valued0.60section
Measurable functionrelated to Non-measurable functionsSuch0.60section

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