 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/26l/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Fatou says

\int lim inf f_{n} \leq lim inf \int f_{n}

for nonnegative functions. Apply it to

g + f_{n}

and

g - f_{n}

when

∣ f_{n} ∣ \leq g \in L^{1}

to obtain both inequalities and hence dominated convergence.

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