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In mathematics, a set function is a function whose input is a set. The output is usually a number. Often the input is a set of real numbers, a set of points in Euclidean space, or a set of points in some measure space. == Examples == Examples of set functions include: * The function that assigns to each set its cardinality, i.e. the number of members of the set, is a set function. * The function :: : assigning densities to sufficiently well-behaved subsets ''A'' ⊆ , is a set function. * The Lebesgue measure is a set function that assigns a non-negative real number to each set of real numbers. (Kolmogorov and Fomin 1975) * A probability measure assigns a probability to each set in a σ-algebra. Specifically, the probability of the empty set is zero and the probability of the sample space is 1, with other sets given probabilities between 0 and 1. * A possibility measure assigns a number between zero and one to each set in the powerset of some given set. See possibility theory. * A Random set is a set-valued random variable. See Random compact set. 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「set function」の詳細全文を読む スポンサード リンク
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