翻訳と辞書 Words near each other ・ Marcin Żewłakow ・ Marcinek ・ Marcinek, Greater Poland Voivodeship ・ Marcinelle ・ Marcinelle school ・ Marcinha ・ Marcinho ・ Marcinho Guerreiro ・ Marciniak ・ Marciniaki ・ Marciniszyn ・ Marcinkevičius ・ Marcinki ・ Marcinkiewicz ・ Marcinkiewicz interpolation theorem ・ Marcinkiewicz–Zygmund inequality ・ Marcinkonys ・ Marcinkonys Ghetto ・ Marcinkowice ・ Marcinkowice, Kazimierza County ・ Marcinkowice, Lower Silesian Voivodeship ・ Marcinkowice, Miechów County ・ Marcinkowice, Nowy Sącz County ・ Marcinkowice, Opatów County ・ Marcinkowice, Tarnów County ・ Marcinkowice, West Pomeranian Voivodeship ・ Marcinkowo ・ Marcinkowo Dolne ・ Marcinkowo Górne ・ Marcinkowo, Braniewo County Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Marcinkiewicz–Zygmund inequality ： ウィキペディア英語版 Marcinkiewicz–Zygmund inequality In mathematics, the Marcinkiewicz–Zygmund inequality, named after Józef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables. It is a generalization of the rule for the sum of variances of independent random variables to moments of arbitrary order. ==Statement of the inequality== Theorem 〔J. Marcinkiewicz and A. Zygmund. Sur les foncions independantes. ''Fund. Math.'', 28:60–90, 1937. Reprinted in Józef Marcinkiewicz, ''Collected papers'', edited by Antoni Zygmund, Panstwowe Wydawnictwo Naukowe, Warsaw, 1964, pp. 233–259. 〕〔Yuan Shih Chow and Henry Teicher. ''Probability theory. Independence, interchangeability, martingales''. Springer-Verlag, New York, second edition, 1988. 〕 If $\backslash textstyle\; x\_$, $\backslash textstyle\; i=1,\backslash ldots,n$, are independent random variables such that $\backslash textstyle\; E\backslash left(\; x\_\backslash right)\; =0$ and , , :$A\_E\backslash left(\; \backslash left(\; \backslash sum\_^\backslash left\backslash vert\; x\_\backslash right\backslash vert\; ^\backslash right)\; \_^\backslash right)\; \backslash leq\; E\backslash left(\; \backslash left\backslash vert\; \backslash sum\_^x\_\backslash right\backslash vert\; ^\backslash right)\; \backslash leq\; B\_E\backslash left(\; \backslash left(\; \backslash sum\_^\backslash left\backslash vert\; x\_\backslash right\backslash vert\; ^\backslash right)\; \_^\backslash right)$ where $\backslash textstyle\; A\_$ and $\backslash textstyle\; B\_$ are positive constants, which depend only on $\backslash textstyle\; p$. 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「Marcinkiewicz–Zygmund 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.