= L2 construction of compensated Poisson integrals
{c}
{title2=$\mathbb E\left|\int f\,(\mu-\nu)\right|^2=\int|f|^2d\nu$}
For deterministic square-integrable $f$ and a <Poisson random measure> of intensity $\nu$, first define the integral for simple functions on disjoint finite-intensity sets. <Independence> and the equality of <Poisson distribution> mean and <variance> prove the displayed <isometry>. Completion defines the integral for all $f\in L^2(\nu)$, even when $\int|f|d\nu=\infty$. A small-jump compensated <martingale> is thereby defined through <convergence in Lp>, not by subtracting two divergent ordinary integrals.
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