Assume $A_j,j\geq 1,j\in\Bbb N$ are measurable sets. Let $m \in N$, and let $E_m$ be the set defined as follows : $x \in E_m \Longleftrightarrow x$ is a member of at least $m$ of the sets $A_k$.
I wanna know how to prove that
- $E_m$ is measurable.
- $m\lambda(E_m)\le\sum^{\infty}_{k=1}\lambda(A_k)$.
It's hard to me. Help me T.T