论文标题
关于正相关的注释
A note on positive association
论文作者
论文摘要
我们表明，如果$ {\ Mathcal a}，{\ Mathcal b}，{\ Mathcal C} $正在增加$ω：= \ {0,1 \}^n $的子集，则使用$ {\ Mathcal a} \ neq \ neq \ emptyset $，然后对任何产品$ { $ \ {{\ MATHCAL A} \ CAP {\ MATHCAL B}，{\ MATHCAL C} \} $，$ \ {{\ MATHCAL A} \ CAP {\ MATHCAL C}是独立的。} \]这意味着对J. Steif的激励问题的答案，并且与该问题的基本，仍然开放的变体有关，以及S. Sahi的众所周知的猜想。
We show that if ${\mathcal A},{\mathcal B},{\mathcal C}$ are increasing subsets of $Ω:=\{0,1\}^n$ with ${\mathcal A}\neq\emptyset$, then with respect to any product probability measure on $Ω$, \[ \mbox{if each of the pairs $\{{\mathcal A}\cap{\mathcal B},{\mathcal C}\}$, $\{{\mathcal A}\cap {\mathcal C},{\mathcal A}\}$ is independent, then ${\mathcal B}$ and ${\mathcal C}$ are independent.} \] This implies an answer to a motivating question of J. Steif, and is related to a basic, still open variant of that question, and to a well-known conjecture of S. Sahi.
