Name: Extensions of set functions
Keywords: Teoria de la, Mesura, Classificació AMS::28 Measure and integration::28A Classical measure theory, extension, algebra of sets, Measures on Boolean rings, measure algebras, Real- or complex-valued set functions, Contents, measures, outer measures, capacities, positive additive set functions, Mesura, Teoria de la

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2003 English Publisher:Universitat Politècnica de Catalunya. Secció de Matemàtiques i InformàticaJournal:Mathware & soft computing

Authors: Ovchinnikov, Sergei V.; Falmagne, Jean-Claude;

handle: 2099/1710

Extensions of set functions

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Abstract

We establish a necessary and suficient condition for a function defined on a subset of an algebra of sets to be extendable to a positive additive function on the algebra. It is also shown that this condition is necessary and sufficient for a regular function defined on a regular subset of the Borel algebra of subsets of a given compact Hausdorff space to be extendable to a measure.

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Teoria de la, Mesura, Classificació AMS::28 Measure and integration::28A Classical measure theory, extension, algebra of sets, Measures on Boolean rings, measure algebras, Real- or complex-valued set functions, Contents, measures, outer measures, capacities, positive additive set functions, Mesura, Teoria de la, :28 Measure and integration::28A Classical measure theory [Classificació AMS], Hausdorff measures, Borel algebra

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