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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 Sigma additivity ： ウィキペディア英語版 Sigma additivity In mathematics, additivity and sigma additivity (also called countable additivity) of a function defined on subsets of a given set are abstractions of the intuitive properties of size (length, area, volume) of a set. == Additive (or finitely additive) set functions == Let ''$\backslash mu$'' be a function defined on an algebra of sets $\backslash scriptstyle\backslash mathcal$ with values in (+∞ ) (see the extended real number line). The function $\backslash mu$ is called additive, or finitely additive, if, whenever ''A'' and ''B'' are disjoint sets in $\backslash scriptstyle\backslash mathcal$, one has :$\backslash mu(A\; \backslash cup\; B)\; =\; \backslash mu(A)\; +\; \backslash mu(B).\; \backslash ,$ (A consequence of this is that an additive function cannot take both −∞ and +∞ as values, for the expression ∞ − ∞ is undefined.) One can prove by mathematical induction that an additive function satisfies : $\backslash mu\backslash left(\backslash bigcup\_^N\; A\_n\backslash right)=\backslash sum\_^N\; \backslash mu(A\_n)$ for any $A\_1,A\_2,\backslash dots,A\_N$ disjoint sets in $\backslash scriptstyle\backslash mathcal$. 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「Sigma additivity」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.