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Set function

In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line R ∪ { ± ∞ } , {\displaystyle \mathbb {R} \cup \{\pm \infty \},} which consists of the real numbers R {\displaystyle \mathbb {R} } and ± ∞ . {\displaystyle \pm…

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Extending set functions

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Set function

Nodes121
Edges120
Triples70
Avg. degree1.98
Density0.016529
Components1

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Set function

Top relations

related to Common properties of set functions · 18
Set function → As, Banach, By, Carathéodory, Carathéodory's, English, Every, For, If, Omega, Outer, Riemann, Since, Stated, That, The, This, Unlike
related to Inner measures, outer measures, and other properties · 8
Set function → Boole's, Every, For, If, In, Lebesgue, Omega, This
related to Lebesgue measure · 8
Set function → Carathéodory, Intervals, Its, Lebesgue, The, The Lebesgue, This, Vitali
related to Extending from semialgebras to algebras · 6
Set function → If, Importantly, Omega, Suppose, The, This
related to Finitely additive translation-invariant set functions · 6
Set function → However, If, In, Omega, The, Theorem
related to Definitions · 5
Set function → If, In, Omega, The, This
related to Further reading · 5
Set function → EMS PressRegular, Encyclopedia, Mathematics, Set, Sobolev
related to Topology related definitions · 5
Set function → Baire, Borel, If, Omega, Radon
related to Examples · 4
Set function → Examples, See, Specifically, The
related to Relationships between set functions · 4
Set function → If, Nikodym, Omega, Radon

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Important terminology

displaystyle mu set measure mathcal infty left right textstyle limits function sum every bigcup mathbb domain additive subseteq series cdots

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Set functionis afunction whose domain is a family of subsets of some given set and that0.90text
Set functionrelated to Common properties of set functionsIf0.60section
Set functionrelated to Common properties of set functionsThe0.60section
Set functionrelated to Common properties of set functionsAs0.60section
Set functionrelated to Common properties of set functionsBy0.60section
Set functionrelated to Common properties of set functionsStated0.60section
Set functionrelated to Common properties of set functionsEnglish0.60section
Set functionrelated to Common properties of set functionsThis0.60section
Set functionrelated to Common properties of set functionsRiemann0.60section
Set functionrelated to Common properties of set functionsSince0.60section
Set functionrelated to Common properties of set functionsThat0.60section
Set functionrelated to Common properties of set functionsOmega0.60section

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