# A Real Analysis question on convergence of functions

Assume $\{f_n\}\subset L^+$, $f_n\rightarrow f$ pointwise, and $\int f=\lim \int f_n < \infty$. Then $\int_E f= \lim \int_E f_n$ for all $E \in M$. However show that this may not be true if $\int f= \lim \int f_n = \infty$

Answers can be viewed only if
1. The questioner was satisfied and accepted the answer, or
2. The answer was disputed, but the judge evaluated it as 100% correct.