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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 Decomposable measure ： ウィキペディア英語版 Decomposable measure In mathematics, a decomposable measure is a measure that is a disjoint union of finite measures. This is a generalization of σ-finite measures, which are the same as those that are a disjoint union of ''countably many'' finite measures. There are several theorems in measure theory such as the Radon–Nikodym theorem that are not true for arbitrary measures but are true for σ-finite measures. Several such theorems remain true for the more general class of decomposable measures. This extra generality is not used much as most decomposable measures that occur in practice are σ-finite. ==Examples== *Counting measure on an uncountable measure space with all subsets measurable is a decomposable measure that is not σ-finite. Fubini's theorem and Tonelli's theorem hold for σ-finite measures but can fail for this measure. *Counting measure on an uncountable measure space with not all subsets measurable is generally not a decomposable measure. *The one-point space of measure infinity is not decomposable. 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「Decomposable 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.