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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 complex measure ： ウィキペディア英語版 complex measure In mathematics, specifically measure theory, a complex measure generalizes the concept of measure by letting it have complex values. In other words, one allows for sets whose size (length, area, volume) is a complex number. == Definition == Formally, a ''complex measure'' $\backslash mu$ on a measurable space $(X,\backslash Sigma)$ is a complex-valued function :$\backslash mu:\; \backslash Sigma\; \backslash to\; \backslash mathbb$ that is sigma-additive. In other words, for any sequence $(A\_)\_^\; \backslash mu(A\_)\; =\; \backslash mu\; \backslash left(\; \backslash bigcup\_^\; A\_\; \backslash right)\; \backslash in\; \backslash mathbb.$ As $\backslash displaystyle\; \backslash bigcup\_^\; A\_\; =\; \backslash bigcup\_^\; A\_$ for any permutation $\backslash sigma:\; \backslash mathbb\; \backslash to\; \backslash mathbb$, it follows that $\backslash displaystyle\; \backslash sum\_^\; \backslash mu(A\_)$ converges unconditionally (hence absolutely). 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「complex 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.