# Math Help - Analysis problem about Holder's inequality

1. ## 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

Can you please give me a hint about how to apply Holder's inequality to this problem? Thanks.

2. ## Re: Analysis problem about Holder's inequality

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"

3. ## Re: Analysis problem about Holder's inequality

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