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Math Help - measure theory

  1. #1
    Junior Member
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    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
    Last edited by Sonifa; April 20th 2014 at 12:46 PM.
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  2. #2
    MHF Contributor
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    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.
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