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How can I show that the measures of preimages of an integrable function converge to zero as $\lambda$ increases? [closed]

I'm trying to show that, for f an integrable, nonnegative measurable function on (X, B), with X finite:

$\lim_{\lambda\rightarrow\infty}\lambda\mu${$x:f(x)>\lambda$}=0$I think in other words I need to show that, if I write a sequence of$\lambda_n$that beyond some n the measure is 0. Or, that f is$\leq\$ some bound a.e.

Also, surely this is trivial for simple functions f.

Would someone give me a tip on where to start?

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This seems like homework, which is not really appropriate for MO. – Qiaochu Yuan Nov 25 2010 at 0:35
The "I think" clause is also incorrect. If it is an actual homework problem, ask the instructor for help. If not, try another web site: some are listed in the FAQ here. – Gerald Edgar Nov 25 2010 at 0:48