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?
