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Pettis integral

In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the case when the measure space is an interval with Lebesgue measure. The…

Properties, Definition & Relation to Dunford integral

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Definition

Relation to Dunford integral

Properties

Law of large numbers for Pettis-integrable random variables

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Pettis integral

Nodes29
Edges28
Triples58
Avg. degree1.93
Density0.068966
Components1

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Pettis integral

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related to References · 36
Pettis integral → America, AMS, Banach, Brooks, Commun, EMS Press, Encyclopedia, Fulltext, Gel'fand, Inst, IV, James, Kharkoff, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Math, Mathematics, Measure Theory, Mecan
related to Properties · 11
Pettis integral → An, Applying, For, Hahn-Banach, If, Lebesgue, Pettis, Phi, Taking, The, This
related to Law of large numbers for Pettis-integrable random variables · 6
Pettis integral → By, Let, Note, Omega, Pettis, Pettis-integrable
related to Mean value theorem · 5
Pettis integral → An, Hahn-Banach, If, Pettis, This

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displaystyle integral pettis mu integrable int varphi vector lebesgue measure space v' every operatorname sigma map measurable text case definition

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SubjectPredicateObjectConfidenceSrc
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesLet0.60section
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesOmega0.60section
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesPettis-integrable0.60section
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesPettis0.60section
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesNote0.60section
Pettis integralrelated to Law of large numbers for Pettis-integrable random variablesBy0.60section
Pettis integralrelated to Mean value theoremAn0.60section
Pettis integralrelated to Mean value theoremPettis0.60section
Pettis integralrelated to Mean value theoremThis0.60section
Pettis integralrelated to Mean value theoremHahn-Banach0.60section
Pettis integralrelated to Mean value theoremIf0.60section
Pettis integralrelated to PropertiesAn0.60section

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