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I don't know why, but I find this problem counter intuitive to me.

Prove that if $\{f_n\}$ is a sequence of measurable nonnegative functions on a measurable set $E$ and $f(x)=\liminf_{n \to \infty} f_{n}(x)$, then

$$\int_{E} f(x) dx \le \liminf_{n \to \infty} \int_{E} f_{n}(x) dx.$$

Can someone outline the proof for me please?

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    Fatou's lemma - proof is givein in Wikipedia's article: http://en.wikipedia.org/wiki/Fatou%27s_lemma#Standard_statement_of_Fatou.27s_lemma2011-12-07
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    haha, how stupid i am. Thx.2011-12-07
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    Alex, maybe you'd care to type up an answer...?2011-12-07

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