Accirding to dominated convergence thm, $\lim_{n\to \infty} \int f_n = \int \lim_{n\to \infty}f_n $
if I choose f f(x)=n if 0<x<1/n and f(x)=0 o.w. then
$ \lim_{n\to\infty} \int f_n = 1, \int \lim_{n\to\infty}f_n =0 $ since $\lim_{n\to\infty}f_n $ is $0$ for almost every x . what's wrong?