f is continuous and

Show that the supremum of f(x) on [a,b] equals

sup f(x) = lim{n->infinity} (1/(b-a) * int[(f(x))^n])^1/n

The integral is from a to b

Latex Attempt:

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- Feb 28th 2009, 09:14 AMKZA459Any ideas on how to show this?
f is continuous and

Show that the supremum of f(x) on [a,b] equals

sup f(x) = lim{n->infinity} (1/(b-a) * int[(f(x))^n])^1/n

The integral is from a to b

Latex Attempt:

- Feb 28th 2009, 09:24 AMAbu-Khalil
This?

It's continuous or not explicit? - Feb 28th 2009, 09:25 AMKZA459
oops and yeah the hypothesis might help eh?

f is cts and

sorry!

yep, this

- Feb 28th 2009, 09:34 AMAbu-Khalil
It's curious 'cause if is continuous then using MVT for integrals you know there exists such as .

So

or not? But if is an increasing function the premise fails :S - Feb 28th 2009, 09:40 AMKZA459
Well I got to that step, but I can't see how that relates to the supremum.

- Feb 28th 2009, 09:42 AMAbu-Khalil
- Feb 28th 2009, 11:03 AMThePerfectHacker
Look here.

- Feb 28th 2009, 11:04 AMKZA459
ah thanks a lot!