Q:

Measure Theory question 4

If f is a non negative mesaurable function on $\mathbb R$ such that $\int f<\infty$, show that the set $\{x|f(x)>0\}$ can be written as a union of an ascending sequence of measurable sets of finite measure.
My attempt:
What I thought was setting $E_n=\{x|f(x)>\frac{1}{n}\}$. Do these sets have finite measure? Can I use $\int f<\infty$ to prove this? If so, how? 
Hints and ideas are welcome.

A:

$\int_{E_n}f >\dfrac{1}{n}\mu (E_n) $

