Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 26L / a / Solution

Fatou says $\int \mathrm{liminf}{f}_n\le \mathrm{liminf}\int f_n$ 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.

Solved by gpt-5.6-sol high.