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Math Help - Continuity and integrability

  1. #1
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    Continuity and integrability

    Let fbe continuous and non-negative on [a,b]. Show that

    (\int_{a}^{b} f^{p})^{1/p} \rightarrowsup f(x) as p\rightarrow\infty
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    You mean (\int_{a}^{b} f^{p})^{1/p} \rightarrow \underset{a \leq x \leq b}{\mbox{sup}} f(x).

    What did you try? Do you have an idea why it's true?
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