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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 Structure theorem for Gaussian measures ： ウィキペディア英語版 Structure theorem for Gaussian measures In mathematics, the structure theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was proved in the 1970s by Kallianpur–Sato–Stefan and Dudley–Feldman–le Cam. There is the earlier result due to H. Satô (1969) 〔(H. Satô, Gaussian Measure on a Banach Space and Abstract Wiener Measure ), 1969.〕 which proves that "any Gaussian measure on a separable Banach space is an abstract Wiener measure in the sense of L. Gross". The result by Dudley et al. generalizes this result to the setting of Gaussian measures on a general topological vector space. ==Statement of the theorem== Let ''γ'' be a strictly positive Gaussian measure on a separable Banach space (''E'', || ||). Then there exists a separable Hilbert space (''H'', ⟨ , ⟩) and a map ''i'' : ''H'' → ''E'' such that ''i'' : ''H'' → ''E'' is an abstract Wiener space with ''γ'' = ''i''∗(''γ''''H''), where ''γ''''H'' is the canonical Gaussian cylinder set measure on ''H''. 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「Structure theorem for Gaussian measures」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.