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Let $f:[0,1] \rightarrow [0,\infty)$ be a measurable function such that:

$\mu (\{x \in [0,1]: f(x) > t \}) \leq \frac{1}{t(ln(t))^{2}}$

holds for each $t>3$.

Show $f$ is an integrable map.

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    Looks like homework. What you have tried?2010-11-13
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    It is not, just practice for the final. That's the problem I don't even know where to start. Any hint?2010-11-13
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    Show that $\int_0^1f(x)\;dx = \int_0^\infty \mu (\{x \in [0,1]: f(x) > t \})\;dt$.2010-11-13

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