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Thread: Analysis problem about Holder's inequality

  1. #1
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    Analysis problem about Holder's inequality

    Suppose that f is a continuous, non-negative function on the interval [0, 1]. Let M be the supremum of f on the interval. Prove that Analysis problem about Holder's inequality-screen-shot-2013-12-07-4.03.40-pm.png


    Can you please give me a hint about how to apply Holder's inequality to this problem? Thanks.
    Last edited by actually; Dec 7th 2013 at 04:24 PM.
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  2. #2
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    Re: Analysis problem about Holder's inequality

    Quote Originally Posted by actually View Post
    Suppose that f is a continuous, non-negative function on the interval [0, 10. Let M be the supremum of f on the interval. Prove that Click image for larger version. 

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    O.K. That is a great question. How can we help you short of just doing it for you?
    Or is your's a command to us: "Prove that"
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  3. #3
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    Re: Analysis problem about Holder's inequality

    Hint: Use the $\displaystyle \leq,\geq$ proof trick for problems like this (one direction is almost trivial here), and prove the (sometimes) easier claim for $\displaystyle \limsup,\liminf$ in the appropriate instances.
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