= Holley inequality
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On a finite distributive configuration lattice, <probability> weights satisfying $\mu_1(\omega\vee\eta)\mu_2(\omega\wedge\eta)\ge\mu_1(\omega)\mu_2(\eta)$ for all pairs give <stochastic domination> $\mu_1\ge\mu_2$. The result holds for nonnegative weights as well: apply the <four functions theorem> to $\mu_1\mathbf1_{A^c},\mu_2\mathbf1_A,\mu_1\mathbf1_A,\mu_2\mathbf1_{A^c}$ for an <increasing event> $A$, obtaining $\mu_1(A^c)\mu_2(A)\le\mu_1(A)\mu_2(A^c)$.
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