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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 G-measure ： ウィキペディア英語版 G-measure In mathematics, a ''G''-measure is a measure $\backslash mu$ that can be represented as the weak-∗ limit of a sequence of measurable functions $G\; =\; \backslash left(G\_n\backslash right)\_^\backslash infty$. A classic example is the ''Riesz product'' : $G\_n(t)\; =\; \backslash prod\_^n\; \backslash left(\; 1\; +\; r\; \backslash cos(2\; \backslash pi\; m^k\; t)\; \backslash right)$ where . The weak-∗ limit of this product is a measure on the circle $\backslash mathbb\; T$, in the sense that for $f\; \backslash in\; C(\backslash mathbb\; T)$: : $\backslash int\; f\; \backslash ,\; d\backslash mu\; =\; \backslash lim\_\; \backslash int\; f(t)\; \backslash prod\_^n\; \backslash left(\; 1\; +\; r\; \backslash cos(2\; \backslash pi\; m^k\; t)\backslash right)\; \backslash ,\; dt\; =\; \backslash lim\_\; \backslash int\; f(t)\; G\_n(t)\; \backslash ,\; dt$ where $dt$ represents Haar measure. The ==History== It was Keane who first showed that Riesz products can be regarded as strong mixing invariant measure under the shift operator $S(x)\; =\; mx\backslash ,\; \backslash bmod\backslash ,\; 1$. These were later generalized by Brown and Dooley to Riesz products of the form : $\backslash prod\_^\backslash infty\; \backslash left(\; 1\; +\; r\_k\; \backslash cos(2\; \backslash pi\; m\_1m\_2\backslash cdots\; m\_k\; t)\; \backslash right)$ where . 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「G-measure」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.