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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 Pre-measure ： ウィキペディア英語版 Pre-measure In mathematics, a pre-measure is a function that is, in some sense, a precursor to a ''bona fide'' measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure. ==Definition== Let ''R'' be a ring of subsets (closed under relative complement) of a fixed set ''X'' and let ''μ''0: ''R'' → () be a set function. ''μ''0 is called a pre-measure if :$\backslash mu\_0(\backslash emptyset)\; =\; 0$ and, for every countable (or finite) sequence ''n''∈N ⊆ ''R'' of pairwise disjoint sets whose union lies in ''R'', :$\backslash mu\_0\; \backslash left\; (\; \backslash bigcup\_^\backslash infty\; A\_n\; \backslash right\; )\; =\; \backslash sum\_^\backslash infty\; \backslash mu\_0(A\_n)$. The second property is called ''σ''-additivity. Thus, what is missing for a pre-measure to be a measure is that it is not necessarily defined on a sigma-algebra (or a sigma-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「Pre-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.