Assume $\displaystyle $A_j,j\geq 1,j\in\Bbb N$$ are measurable sets. Let $\displaystyle $m \in N$$, and let $\displaystyle $E_m$$ be the set defined as follows : $\displaystyle $x \in E_m \Longleftrightarrow x$$ is a member of at least $m$ of the sets $\displaystyle $A_k$$.

I wanna know how to prove that

1. $\displaystyle $E_m$$ is measurable.

2. $\displaystyle $m\lambda(E_m)\le\sum^{\infty}_{k=1}\lambda(A_k)$$.

Thank you for your help.