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View Full Version : Integrals, L^p-spaces, weak convergence


brian_m.
Nov20-11, 04:55 AM
Hi,



let g \in L^\infty(\mathbb R) with g(x+1)=g(x) in \mathbb R and \int_0^1 g(t)dt =\lambda.

Then for f_n(x)=g(nx) the sequence f_n converges weakly to \lambda in L^p(I) , whereas 1<p<\infty and I denotes an open, bounded intervall.

How to prove this?
Thanks in advance for your help!

Bye,
brian