D3
= D3
{c}
{scope}
The <monotone convergence theorem> states that if nonnegative measurable functions $h_n$ increase <almost everywhere> to $h$, then $\int h=\lim_n\int h_n$, allowing infinity. The <dominated convergence theorem> states that if measurable $h_n\to h$ <almost everywhere> and $|h_n|\le g$ for an <integrable> $g$, then $h$ is <integrable> and $\int h_n\to\int h$.