= Stationary point process
{title2=$\Pi(\,\cdot+h)\overset{d}{=}\Pi$}
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 $\rho\ge0$, 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>.<Lectures on the Poisson Process by Günter Last and others>[Section 8.1, Proposition 8.2, printed pp. 69-70: stationarity and constant intensity under a finite unit-cube mean]{ref}
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