Timeline for Measure theory treatment geared toward the Riesz representation theorem

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Mar 10, 2014 at 21:38	comment	added	Tom LaGatta		@jbc, could you please share the definition of a $k_R$ space? I tried to find it in the literature but couldn't.
Nov 11, 2012 at 6:47	comment	added	jbc		Buck uses weighted seminorms, i.e., he multiplies bounded, continuous functions by ones which vanish at infinity, then takes the supremum norm. This has the effect of cutting out the parts of the measures which live on the boundary. In the non locally compact case one mixes (in the sense of the polish school) the norm and the topology of compact convergence. It follows from the general theory that the new dual is the closure of that of the latter in the former, i.e., one gets those measures on the compactification which are approximable by ones with compact support and this is just right.
Nov 10, 2012 at 22:08	comment	added	Igor Khavkine		Thanks for this interesting contribution! Although it's so information dense that it's hard to absorb in one reading. A quick question though. If, as you say, Buck worked with the dual of $C^b(X)$, is that not the same as working with the dual of $C(\beta X)$, where $\beta$ denotes Stone-Cech compactification? Or does his special choice of topology on $C^b(X)$ makes its topological dual identical with that of $C(X)$, with respect to some reasonable topology on the latter?
Nov 10, 2012 at 19:00	history	edited	jbc	CC BY-SA 3.0	made one statement more precise
Nov 10, 2012 at 14:09	history	answered	jbc	CC BY-SA 3.0