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In mathematics, the support of a function is the set of points where the function is not zero-valued or, in the case of functions defined on a topological space, the closure of that set. This concept is used very widely in mathematical analysis. In the form of functions with support that is bounded, it also plays a major part in various types of mathematical duality theories. ==Formulation== Suppose that ''f'' : ''X'' → R is a real-valued function whose domain is an arbitrary set ''X''. The set-theoretic support of ''f'', written supp(''f''), is the set of points in ''X'' where ''f'' is non-zero : The support of ''f'' is the smallest subset of ''X'' with the property that ''f'' is zero on the subset's complement, meaning that the non-zero values of ''f'' "live" on supp(f). If ''f''(''x'') = 0 for all but a finite number of points ''x'' in ''X'', then ''f'' is said to have finite support. If the set ''X'' has an additional structure (for example, a topology), then the support of ''f'' is defined in an analogous way as the smallest subset of ''X'' of an appropriate type such that ''f'' vanishes in an appropriate sense on its complement. The notion of support also extends in a natural way to functions taking values in more general sets than R and to other objects, such as measures or distributions. 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「Support (mathematics)」の詳細全文を読む スポンサード リンク
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