With s>1 and r>s. How can I show that , for expectation with respect to a probability measure?

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- November 26th 2010, 09:45 PMnoob mathematicianHolder's inequality
With s>1 and r>s. How can I show that , for expectation with respect to a probability measure?

- November 27th 2010, 08:38 AMMoo
Hello,

Show what you've done. Basically, you just have to apply Holder's inequality to , with as f and 1 as g. If X is in then , that's how it'll work.

Give it a try. - November 28th 2010, 01:24 AMnoob mathematician
Holder inequality:

Let q=r/s

with r.v.

Then ?

Not very sure though - November 28th 2010, 04:23 AMMoo
This is exactly it ! (Clapping)

Now you have to talk a little :

Let's take . Then . - your calculations - . Thus , which implies that : any element of the first belongs to the second.