Hi,

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

I have a solution but I do not see it:

$\displaystyle \{ x \in X | z(x)>a \}= \cup_{n=1}^{\infty} \{x \in X| f_n(x)>a \} $