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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 '''' be a function defined on an algebra of sets with values in (+∞ ) (see the extended real number line). The function is called additive, or finitely additive, if, whenever ''A'' and ''B'' are disjoint sets in , one has : (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 : for any disjoint sets in . 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
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