翻訳と辞書 Words near each other ・ Borg-Warner 35 transmission ・ Borg-Warner T-5 transmission ・ Borg-Warner T-50 transmission ・ Borg-Warner T-56 transmission ・ Borg-Warner T-90 ・ Borg-Warner Trophy ・ Borgal ・ Borgan ・ Borgan, Fars ・ Borgang ・ Borgaon Dam ・ Borgaon Manju ・ Borgarbyggð ・ Borgarello ・ Borello ・ Borell–Brascamp–Lieb inequality ・ Borel–Cantelli lemma ・ Borel–Carathéodory theorem ・ Borel–de Siebenthal theory ・ Borel–Kolmogorov paradox ・ Borel–Moore homology ・ Borel–Weil theorem ・ Borel–Weil–Bott theorem ・ Boreman ・ Boreman Hall ・ Boreman, West Virginia ・ Boremshchyna ・ Boren ・ Boren (surname) ・ Boren (Sweden) 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 Borell–Brascamp–Lieb inequality ： ウィキペディア英語版 Borell–Brascamp–Lieb inequality In mathematics, the Borell–Brascamp–Lieb inequality is an integral inequality due to many different mathematicians but named after Christer Borell, Herm Jan Brascamp and Elliott Lieb. The result was proved for ''p'' > 0 by Henstock and Macbeath in 1953. The case ''p'' = 0 is known as the Prékopa–Leindler inequality and was re-discovered by Brascamp and Lieb in 1976, when they proved the general version below; working independently, Borell had done the same in 1975. The nomenclature of "Borell–Brascamp–Lieb inequality" is due to Cordero-Erausquin, McCann and Schmuckenschläger, who in 2001 generalized the result to Riemannian manifolds such as the sphere and hyperbolic space. ==Statement of the inequality in R''n''== Let 0 < ''λ'' < 1, let −1 / ''n'' ≤ ''p'' ≤ +∞, and let ''f'', ''g'', ''h'' : R''n'' → [0, +∞) be integrable functions such that, for all ''x'' and ''y'' in R''n'', :$h\; \backslash left(\; (1\; -\; \backslash lambda)\; x\; +\; \backslash lambda\; y\; \backslash right)\; \backslash geq\; M\_\; \backslash left(\; f(x),\; g(y),\; \backslash lambda\; \backslash right),$ where :$$ \begin M_ (a, b, \lambda)& = \left( (1 - \lambda) a^ + \lambda b^ \right)^,\\ M_ (a, b, \lambda)& = a^ b^.\, \end Then :$\backslash int\_\}\; h(x)\; \backslash ,\; \backslash mathrm\; x\; \backslash geq\; M\_\; \backslash left(\; \backslash int\_\}\; f(x)\; \backslash ,\; \backslash mathrm\; x,\; \backslash int\_\}\; g(x)\; \backslash ,\; \backslash mathrm\; x,\; \backslash lambda\; \backslash right).$ (When ''p'' = −1 / ''n'', the convention is to take ''p'' / (''n'' ''p'' + 1) to be −∞; when ''p'' = +∞, it is taken to be 1 / ''n''.) 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「Borell–Brascamp–Lieb 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.