Integrable envelope of a function class
= Integrable envelope of a function class
{title2=$|h|\le M,\quad PM<\infty$}
A measurable function $M$ is an <integrable envelope of a function class> for a class $\mathcal H$ under a probability law $P$ if $|h(x)|\le M(x)$ for every $h\in\mathcal H$ and $PM<\infty$. Such an envelope permits the <dominated convergence theorem> to control shrinking <function brackets>.