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
Last edited by Sonifa; Apr 20th 2014 at 12:46 PM.
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If $\displaystyle f(x)<0$ for all $\displaystyle x\in \mathbb{R}$, then that limit is zero. However, that in no way implies that $\displaystyle \int |f|dm$ exists much less is finite.
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