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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 Carathéodory's extension theorem ： ウィキペディア英語版 Carathéodory's extension theorem :''See also Carathéodory's theorem for other meanings.'' In measure theory, Carathéodory's extension theorem (named after the Greek mathematician Constantin Carathéodory) states that any measure defined on a given ring ''R'' of subsets of a given set ''Ω'' can be extended to the σ-algebra generated by ''R'', and this extension is unique if the measure is σ-finite. Consequently, any measure on a space containing all intervals of real numbers can be extended to the Borel algebra of the set of real numbers. This is an extremely powerful result of measure theory, and proves, for example, the existence of the Lebesgue measure. == Semi-ring and ring == 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「Carathéodory's extension theorem」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.