= Progressive measurability
= Progressively measurable
{synonym}
= Progressively measurable process
{synonym}
A process $H$ is progressively measurable when, for every $T$, its restriction to $[0,T]\times\Omega$ is measurable for $\mathcal B([0,T])\otimes\mathcal F_T$. Continuous <adapted processes> are progressively measurable, and a Borel <function> of such a process remains so. A progressively measurable square-integrable Brownian integrand has an equivalent <predictable process>[predictable] integrand for the <Itô integral>, up to equality for $dt\,d\mathbb P$.
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