# Math Help - measure theory

1. ## measure theory

Let f be a measurable function. Assume that

lim λm({x|f(x)>λ}) exists and is finite as λ tends to infinite

Does this imply that ∫|f|dm is finite?

Here m is the Lebesgue measure in R

2. ## Re: measure theory

If $f(x)<0$ for all $x\in \mathbb{R}$, then that limit is zero. However, that in no way implies that $\int |f|dm$ exists much less is finite.