I don't know why, but I find this problem counter intuitive to me.
Prove that if $\{f_n\}$ is a sequence of measurable nonnegative functions on a measurable set $E$ and $f(x)=\liminf_{n \to \infty} f_{n}(x)$, then
$\int_{E} f(x) dx \le \liminf_{n \to \infty} \int_{E} f_{n}(x) dx.$
Can someone outline the proof for me please?