= Stochastic domination of probability measures
{title2=$\mu\preceq\nu$}
On a finite partially ordered state space, $\mu\preceq\nu$ means $\int f\,d\mu\leq\int f\,d\nu$ for every real-valued <order-preserving function> $f$. Equivalently, every increasing subset has no larger <probability> under $\mu$ than under $\nu$. A coupling supported on pairs $(X,Y)$ with $X\leq Y$ proves this relation. This concerns order of <probability> laws, rather than stochastic asymptotic order notation.
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