Intersection of union of measurable set Let $f_n$ be a sequence of measurable functions on $\mathbb R$.  
Show that the set $A:= \{x \in \mathbb R \mid f_n > 0\text{ for infinitely many } n \}$ is measurable.
If I write the set $A$ like intersection of the union of a measurable set, then I am done. 
But I can not. 
Please help me. 

Let $$E_n:= \{f_n > 0\}=\{x\in\mathbb R\mid f_n(x)>0\}$$
$$A = \bigcap_{n=1}^\infty \bigcup_{k=n}^\infty E_n$$
