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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Perfect measure ： ウィキペディア英語版 Perfect measure In mathematics — specifically, in measure theory — a perfect measure (or, more accurately, a perfect measure space) is one that is “well-behaved” in some sense. Intuitively, a perfect measure ''μ'' is one for which, if we consider the pushforward measure on the real line R, then every measurable set is “''μ''-approximately a Borel set”. The notion of perfectness is closely related to tightness of measures: indeed, in metric spaces, tight measures are always perfect. ==Definition== A measure space (''X'', Σ, ''μ'') is said to be perfect if, for every Σ-measurable function ''f'' : ''X'' → R and every ''A'' ⊆ R with ''f''−1(''A'') ∈ Σ, there exist Borel subsets ''A''1 and ''A''2 of R such that :$A\_\; \backslash subseteq\; A\; \backslash subseteq\; A\_\; \backslash mbox\; \backslash mu\; \backslash big(\; f^\; (\; A\_\; \backslash setminus\; A\_\; )\; \backslash big)\; =\; 0.$ 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「Perfect measure」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.