= Campbell first-moment formula
{c}
{title2=$\mathbb E\sum_{z\in\Pi}h(z)=\int h\,d\mu$}
For a <Poisson random measure> $\Pi$ with intensity $\mu$ and measurable nonnegative $h$, $\mathbb E\int h\,d\Pi=\int h\,d\mu$, allowing both sides to be infinite. For signed $h$, the same identity holds if $\int|h|d\mu<\infty$. This first-moment statement does not require square integrability. Applying it to a nonnegative <volume> mark gives the expected total <volume> in a marked Poisson model.
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