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Math Help - Lebesgue Spaces Inclusion

  1. #1
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    Lebesgue Spaces Inclusion

    Need help with the following:

    Show that (L_p(E) \cap L_{\infty}(E)) \subset L_q if 1 \leq p < q < \infty.

    (I am talking about Lebesgue spaces as in here: Lp space - Wikipedia, the free encyclopedia)

    Thanks!
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  2. #2
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     \int f^q d\mu=\int f^p f^{q-p} d\mu \leq ||f^{q-p}||_\infty \int f^p d\mu
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