I was wondering how to prove a given space is separable or not. take L^2 and L^\infty for example please ! Any idea or help is appreciated !
Last edited by Shanks; Nov 21st 2009 at 08:59 AM. Reason: add details
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For you could use the fact that it's a Hilbert space, and that a Hilbert space is separable iff it has a countable orthonormal basis. is not so easy as the continous functions are not dense!
Last edited by Jose27; Nov 21st 2009 at 09:58 AM.
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