Exercise 14, § 4

Let $(A_n)$ be a sequence of integrable sets such that $\sum_n \mu(A_n) < +\infty$. For every integer $k$, let $G_k$ be the set of $x \in X$ such that $x \in A_n$ for at least $k$ values of $n$; show that $G_k$ is integrable and that $k \cdot \mu(G_k) \leqslant \sum_n \mu(A_n)$.