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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 Closed convex function ： ウィキペディア英語版 Closed convex function In mathematics, a function $f:\; \backslash mathbb^n\; \backslash rightarrow\; \backslash mathbb$ is said to be closed if for each $\backslash alpha\; \backslash in\; \backslash mathbb$, the sublevel set $\backslash$ is a closed set. Equivalently, if the epigraph defined by $\backslash mbox\; f\; =\; \backslash \; \backslash vert\; x\; \backslash in\; \backslash mbox\; f,\backslash ;\; f(x)\; \backslash leq\; t\backslash \}$ is closed, then the function $f(x)$ is closed. This definition is valid for any function, but most used for convex function. A proper convex function is closed if and only if it is lower semi-continuous. For a convex function which is not proper there is disagreement as to the definition of the ''closure'' of the function. == Properties == * If $f:\; \backslash mathbb^n\; \backslash rightarrow\; \backslash mathbb$ is a continuous function and $\backslash mbox\; f$ is closed, then $f$ is closed. * A closed proper convex function ''f'' is the pointwise supremum of the collection of all affine functions ''h'' such that ''h'' ≤ ''f'' (called the affine minorants of ''f''). 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「Closed convex function」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.