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If an integrable function $f(x)\ge0$ a.e., then $\int fd\mu\ge0$. Any hint is appreciated.

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    Suppose not ...2012-12-10
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    Sorry, I still cannot figure it out.2012-12-10
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    Would be you be able to prove the statement if $f(x) \geq 0$ instead of $f(x) \geq 0$ a.e. ? (This is such a fundamental question, that we need to know exactly where you are having trouble to provide useful comments)2012-12-10
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    Use the definition of the integral, it will follow directly.2012-12-10
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    What is the definition of $\int f d\mu$?2012-12-10
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    @Sam you can post you comment as an answer.2012-12-10

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