Talk:ba space

Untitled[edit]

I have reservations about this article. On the one hand, I've never looked at finitely additive set functions. Still, many of the "properties" look suspicious or lack clarity. I would like to have a reference and proof sketches, especially for the statement about the dual of l^infinity. Loisel 22:38, 27 Jun 2004 (UTC)

Okay, in the Lp spaces discussion, the isomorphism has been clarified and even shown to apply to L^infinity. I still think that the isomorphism should be described in this article, because I had the wrong idea when I was trying to figure out what it should be. Loisel 19:54, 30 Jun 2004 (UTC)

The article currently says "If Σ is a sigma-algebra and μ is a sigma-additive positive measure on Σ then the Lp space L^∞(μ) endowed with the essential supremum norm is by definition the quotient space of B(Σ) by the closed subspace of bounded μ-null functions". I don't think this is correct. The dual space might be the stated quotient space but, *by definition*, the dual space is the space of continuous linear functions on $L^\infty$. 129.215.104.157 (talk) 12:48, 25 July 2017 (UTC)[reply]

rca space[edit]

I followed a wikilink to "rca space", which redirected me to "ba space". But the ba space article makes no mention of any rca space. So what's rca space? Is it the same thing, or an older term for the same thing, or something slightly different? Could somebody (perhaps whoever ordered or okayed the redirection, for example) PLEASE define "rca space" within the "ba space" article ! Or recreate the alternative page. Either/or, for clarity, so that the term makes sense rather than just leaving a mystery. Pete Hobbs (talk) 16:47, 27 April 2013 (UTC)[reply]