Measurable space

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A set with a distinguished ring or -ring (in particular, an algebra or a -algebra) of subsets of .

Examples: with the ring of Jordan-measurable sets (see Jordan measure); with the -ring of sets of finite Lebesgue measure; a topological space with the -algebra of Borel sets (cf. Borel set).


[1] P.R. Halmos, "Measure theory" , v. Nostrand (1950)
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Measurable space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.V. Sazonov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article