can somebody explain me this equality please
{ω : g(ω) ≤ r} =$\bigcup^\infty_{n=1}${ω : $f_{n}$(ω) ≤ r}
where $g=\sup_{n\geq 1} f_n$
this is to prove that the supremum of mesurable sequences is mesurable too but i can't understand where the equality came from.