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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 Radonifying function ： ウィキペディア英語版 Radonifying function In measure theory, a radonifying function (ultimately named after Johann Radon) between measurable spaces is one that takes a cylinder set measure (CSM) on the first space to a true measure on the second space. It acquired its name because the pushforward measure on the second space was historically thought of as a Radon measure. ==Definition== Given two separable Banach spaces $E$ and $G$, a CSM $\backslash \; (E)\; \backslash \}$ on $E$ and a continuous linear map $\backslash theta\; \backslash in\; \backslash mathrm\; (E;\; G)$, we say that $\backslash theta$ is ''radonifying'' if the push forward CSM (see below) $\backslash left\backslash )\; \backslash right)\_\; \backslash right|\; S\; \backslash in\; \backslash mathcal\; (G)\; \backslash right\backslash \}$ on $G$ "is" a measure, i.e. there is a measure $\backslash nu$ on $G$ such that ::$\backslash left(\; \backslash theta\_\; (\backslash mu\_)\; \backslash right)\_\; =\; S\_\; (\backslash nu)$ for each $S\; \backslash in\; \backslash mathcal\; (G)$, where $S\_\; (\backslash nu)$ is the usual push forward of the measure $\backslash nu$ by the linear map $S\; :\; G\; \backslash to\; F\_$. 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「Radonifying 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.