= Density of simple predictable processes for finite measures
{title2=$\overline{\mathcal S}^{\,L^2(\mu)}=L^2(\mathcal P,\mu)$}
For every <finite measure> $\mu$ on the <predictable sigma-algebra>, bounded <simple predictable processes> are dense in $L^2(\mu)$. Include a bounded $\mathcal F_0$-measurable value supported at time zero when $\mu$ may charge that slice. Indicators of the generating rectangles and the <Pi-lambda theorem> prove density. This gives the completion step in the <Itô isometry> construction.
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