Timeline for Measure theory treatment geared toward the Riesz representation theorem
Current License: CC BY-SA 3.0
17 events
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| Dec 6, 2017 at 8:22 | comment | added | Igor Khavkine | @AlexM., I asked this question long enough ago that I don't recall whether I excluded the locally compact hypothesis on purpose or by accident. However, I think that it would be really useful to have a small list of references on such a general version of the theorem, especially since it doesn't seem to be so well-known. At least I'd appreciate it! | |
| Dec 5, 2017 at 20:11 | comment | added | Alex M. | @IgorKhavkine: Since you do not seem to require $X$ to be locally-compact, I doubt that you will find what you want in books. This is because it requires the use of the strict topology, which isn't quite a mainstream tool. There are, though, plenty of articles treating the general case of $X$ Hausdorff and completely regular, and if this is of interest to you I might be able to compile a small list of references. | |
| Nov 10, 2012 at 14:09 | answer | added | jbc | timeline score: 7 | |
| Aug 24, 2012 at 19:05 | answer | added | Dick Palais | timeline score: 1 | |
| Aug 24, 2012 at 18:08 | answer | added | Ljubomir Cukic | timeline score: 1 | |
| Aug 24, 2012 at 11:08 | history | edited | Igor Khavkine | CC BY-SA 3.0 |
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| Aug 22, 2012 at 0:00 | history | edited | Igor Khavkine | CC BY-SA 3.0 |
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| Aug 21, 2012 at 19:39 | answer | added | user23860 | timeline score: 3 | |
| Aug 21, 2012 at 16:21 | comment | added | Paul Siegel | My favorite exposition of the Riesz representation theorem for $C_0(X)$, $X$ locally compact, is in Folland's chapter on Radon measures. The proof is very detailed. | |
| Aug 21, 2012 at 10:46 | comment | added | Igor Khavkine | @Michael, thanks a lot. I should definitely look these up. Feel free to repost as an answer! | |
| Aug 21, 2012 at 10:45 | comment | added | Igor Khavkine | @Yemon, according to Dunford & Schwartz, $C^*(X)$ is the space of "regular, bounded, (finitely) additive" set functions. I'm still trying to sort out what this means and how it relates to the topology on $C(X)$. | |
| Aug 21, 2012 at 10:30 | comment | added | Michael Greinecker | I think you can find these results in Aliprantis & Border, Infinite Dimensional Analysis (3rd ed). The book has a whole chapter on Riesz representation theorem. A hard to read book that probbly contains everything there is to know is Fremlin, Topological Riesz Spaces and Measure Theory. | |
| Aug 21, 2012 at 10:09 | comment | added | Yemon Choi | Hang on, what is the RRT for C(X) when X is non-compact? | |
| Aug 21, 2012 at 9:51 | answer | added | LeBlanc | timeline score: 3 | |
| Aug 21, 2012 at 9:30 | comment | added | Igor Khavkine | Don't know. Will check... That's why I'm asking. :-) | |
| Aug 21, 2012 at 9:13 | comment | added | Yemon Choi | Comment only, since I am not sure: is the account in Rudin's RCA general enough for your purposes? | |
| Aug 21, 2012 at 9:09 | history | asked | Igor Khavkine | CC BY-SA 3.0 |