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Possible Duplicate:
convergence in $L^1$ norm
Convergence of Lebesgue integrals

let $f$ and $f_n,n\geq 1$ be integrable functions on $X$. Suppose that $f_n \to f$ a.e. on $X$ as $n\to \infty$, and $\int_X f_n d\mu \to \int_X fd\mu$ as $n\to \infty$. Show that if every $f_n \geq 0$ a.e. on $X$, then $ \lim_{n\to\infty} \int_X |f_n -f|d\mu = 0 .$

Please how do I begin? Thanks

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    And all [this](http://math.stackexchange.com/q/83208/8271) sort of questions can be answered by [this one](http://math.stackexchange.com/q/51502/8271)2012-04-19

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