Hi,
I need to prove that z(x)=sup \{f_n(x): n \in N   \} is measurable function where  f_n are measurable function and f_n : X -> R

I have a solution but I do not see it:
 \{ x \in X | z(x)>a  \}= \cup_{n=1}^{\infty} \{x \in X| f_n(x)>a  \}