Solution
= Solution
The <dominated convergence theorem> states that, on a measure space, if measurable $f_n\to f$ almost everywhere and $|f_n|\leq g$ almost everywhere for one integrable $g$, then $f$ is integrable and $\int|f_n-f|\to0$. In particular, \b[$\int f_n\to\int f$]. The statement applies to real or complex functions.