Solution
= Solution
Fatou says $\int\liminf f_n\le\liminf\int f_n$ for nonnegative <functions>. Apply it to $g+f_n$ and $g-f_n$ when $|f_n|\le g\in L^1$ to obtain both inequalities and hence dominated convergence.
= Solution
Fatou says $\int\liminf f_n\le\liminf\int f_n$ for nonnegative <functions>. Apply it to $g+f_n$ and $g-f_n$ when $|f_n|\le g\in L^1$ to obtain both inequalities and hence dominated convergence.