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Math Help - Integrable Function

  1. #1
    Junior Member
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    Integrable Function

    Let (X,M, \mu) be a measure space and let f\in L^{+} be integrable ( \int f d\mu< \infty). Show that for each \epsilon > 0 there is a \delta > 0 such that if A \subset X and \mu(A)< \delta,
    then \int f<  \epsilon where the integral is calculate over the subset A. Show that the result may fail if the assumption on the integrability of f is dropped.
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  2. #2
    Super Member girdav's Avatar
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    Re: Integrable Function

    First, consider the case for which f is a simple function.
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