If an integrable function $f(x)\ge0$ a.e., then $\int fd\mu\ge0$. Any hint is appreciated.
How to prove this problem about integrable function?
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measure-theory
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2Suppose not ... – 2012-12-10
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0Sorry, I still cannot figure it out. – 2012-12-10
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0Would 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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0Use the definition of the integral, it will follow directly. – 2012-12-10
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0What is the definition of $\int f d\mu$? – 2012-12-10
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0@Sam you can post you comment as an answer. – 2012-12-10