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 $\int f= \lim \int f_n = \infty$


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