Re: cl(bigcap_{1<=q<=infty} L^q) = L^p

From: Kira Yamato <no@xxxxxxxx>
Date: Fri, 27 May 2005 01:29:02 GMT

Ok, thanks to everyone who replied. So, the proof is ok for 1<=q<infty, but not when q=infty, even though the conclusion is true including q=infty if instead we consider Cc(R) as stated by Martin.

-kira

Martin wrote:

If we denote by Cc(R) all continuous functions with compact support,
then the set Cc(X) is dense subset of L^p. (Rudin: Real and Complex
Analysis, Theorem 3.14)
Since Cc(X) belongs to each L^p, we arrive to your conclusion - this is
another possibility for the proof.
Martin

Follow-Ups:
- Re: cl(bigcap_{1<=q<=infty} L^q) = L^p
  - From: David C . Ullrich

References:
- cl(bigcap_{1<=q<=infty} L^q) = L^p
  - From: Kira Yamato
- Re: cl(bigcap_{1<=q<=infty} L^q) = L^p
  - From: Martin

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