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In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets. ==Definition== Let (''X'', ''T'') be a Hausdorff topological space and let Σ be a σ-algebra on ''X'' that contains the topology ''T'' (so that every open set is a measurable set, and Σ is at least as fine as the Borel σ-algebra on ''X''). Then a measure ''μ'' on the measurable space (''X'', Σ) is called inner regular if, for every set ''A'' in Σ, : This property is sometimes referred to in words as "approximation from within by compact sets." Some authors〔 〕 use the term tight as a synonym for inner regular. This use of the term is closely related to tightness of a family of measures, since a measure ''μ'' is inner regular if and only if, for all ''ε'' > 0, there is some compact subset ''K'' of ''X'' such that ''μ''(''X'' \ ''K'') < ''ε''. This is precisely the condition that the singleton collection of measures is tight. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「inner regular measure」の詳細全文を読む スポンサード リンク
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