 Stationary point process

A point process on ${\mathbb{R}}^d$ is stationary if every translation preserves its probability law. If its mean count in a unit cube is finite, its intensity measure is $\mu (A)=\rho |A|$ for some $\rho \ge 0$, where $|A|$ denotes Lebesgue measure. This follows because stationarity makes the mean measure invariant under translations. A constant intensity function of a point process describes only these mean counts, and by itself asserts neither stationarity of the entire law nor independence.^[ref]