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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 Fernique's theorem ： ウィキペディア英語版 Fernique's theorem In mathematics — specifically, in measure theory — Fernique's theorem is a result about Gaussian measures on Banach spaces. It extends the finite-dimensional result that a Gaussian random variable has exponential tails. The result was proved in 1970 by the mathematician Xavier Fernique. ==Statement of the theorem== Let (''X'', || ||) be a separable Banach space. Let ''μ'' be a centered Gaussian measure on ''X'', i.e. a probability measure defined on the Borel sets of ''X'' such that, for every bounded linear functional ''ℓ'' : ''X'' → R, the push-forward measure ''ℓ''∗''μ'' defined on the Borel sets of R by :$(\; \backslash ell\_\; \backslash mu\; )\; (A)\; =\; \backslash mu\; (\; \backslash ell^\; (A)\; ),$ is a Gaussian measure (a normal distribution) with zero mean. Then there exists ''α'' > 0 such that : ''A fortiori'', ''μ'' (equivalently, any ''X''-valued random variable ''G'' whose law is ''μ'') has moments of all orders: for all ''k'' ≥ 0, : 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「Fernique's theorem」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.