= Square-integrable martingale
{title2=$\mathbb E|M_t|^2<\infty\text{ for every finite }t$}
A <martingale> is square integrable when its value at every time belongs to <L2 space>. This implies ordinary integrability by <Cauchy-Schwarz inequality>. The condition is separate from a uniform bound on these second moments over an infinite horizon. An <Itô integral> is square integrable on a finite interval when its predictable integrand has finite expected integrated square, by <Itô isometry>.
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