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Characteristic function (convex analysis) : ウィキペディア英語版 | Characteristic function (convex analysis)
In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non-membership) of a given element in that set. It is similar to the usual indicator function, and one can freely convert between the two, but the characteristic function as defined below is better-suited to the methods of convex analysis. ==Definition==
Let be a set, and let be a subset of . The characteristic function of is the function : taking values in the extended real number line defined by :
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