= Moments of a marked Poisson integral
{title2=$\mathbb E W=\int m\,d\mu,\quad\operatorname{Var}W=\int(v+m^2)\,d\mu$}
Attach conditionally <independent> nonnegative marks to a <Poisson point process>, with a <measurable> mark law depending only on location. If a mark at $z$ has <mean> $m(z)$ and <variance> $v(z)$, and the displayed <integrals> are finite, their total $W$ is finite <almost surely> and has the displayed moments. The <Campbell first-moment formula> gives the first moment and finiteness. The <Poisson factorial moment measure> formula gives the square of that first moment for distinct pairs; the diagonal contributes $\int(v+m^2)\,d\mu$. Their difference is the <variance>. Signed marks require absolute first-moment integrability.
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