With s>1 and r>s. How can I show that , for expectation with respect to a probability measure?
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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.
Holder inequality: Let q=r/s with r.v. Then ? Not very sure though
This is exactly it ! 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.
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