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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 Ahlswede–Daykin inequality ： ウィキペディア英語版 Ahlswede–Daykin inequality A fundamental tool in statistical mechanics and probabilistic combinatorics (especially random graphs and the probabilistic method), the Ahlswede–Daykin inequality , also known as the four functions theorem (or inequality), is a correlation-type inequality for four functions on a finite distributive lattice. It states that if $f\_1,f\_2,f\_3,f\_4$ are nonnegative functions on a finite distributive lattice such that :$f\_1(x)f\_2(y)\backslash le\; f\_3(x\backslash vee\; y)f\_4(x\backslash wedge\; y)$ for all ''x'', ''y'' in the lattice, then :$f\_1(X)f\_2(Y)\backslash le\; f\_3(X\backslash vee\; Y)f\_4(X\backslash wedge\; Y)$ for all subsets ''X'', ''Y'' of the lattice, where :$f(X)\; =\; \backslash sum\_f(x)$ and :$X\backslash vee\; Y\; =\; \backslash$ :$X\backslash wedge\; Y\; =\; \backslash .$ The Ahlswede–Daykin inequality can be used to provide a short proof of both the Holley inequality and the FKG inequality. It also implies the Fishburn–Shepp inequality. For a proof, see the original article or . ==Generalizations== The "four functions theorem" was independently generalized to 2''k'' functions in and . 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「Ahlswede–Daykin 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.