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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 Khintchine inequality ： ウィキペディア英語版 Khintchine inequality In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Roman alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick $N$ complex numbers $x\_1,\backslash dots,x\_N\; \backslash in\backslash mathbb$, and add them together each multiplied by a random sign $\backslash pm\; 1$, then the expected value of its modulus, or the modulus it will be closest to on average, will be not too far off from $\backslash sqrt\}$. ==Statement of theorem== Let $\backslash \_^$ be i.i.d. random variables with $P(\backslash epsilon\_n=\backslash pm1)=\backslash frac12$ for every $n=1\backslash ldots\; N$, i.e., a sequence with Rademacher distribution. Let Then :$A\_p\; \backslash left(\; \backslash sum\_^|x\_|^\; \backslash right)^\}\; \backslash leq\; \backslash left(\backslash mathbb\backslash Big|\backslash sum\_^\backslash epsilon\_x\_\backslash Big|^\; \backslash right)^\; \backslash leq\; B\_p\; \backslash left(\backslash sum\_^|x\_|^\backslash right)^\}$ for some constants $A\_p,B\_p>0$ depending only on $p$ (see Expected value for notation). The sharp values of the constants $A\_p,B\_p$ were found by Haagerup (Ref. 2; see Ref. 3 for a simpler proof). It is a simple matter to see that $A\_p\; =\; 1$ when $p\; \backslash ge\; 2$, and $B\_p\; =\; 1$ when . 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「Khintchine inequality」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.