Increasing function on a partially ordered set ($\omega \le \eta ⟹f(\omega )\le f(\eta )$)

A real-valued function on a partially ordered set is increasing when it preserves its order. Indicators of increasing events are examples. In spin or edge configuration spaces the order is coordinatewise, so increasing observables grow when a zero coordinate is replaced by one. Positive association of random variables concerns pairs of such observables, and stochastic domination compares their expectations.