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 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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Originally Posted by actually 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 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"
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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