Timeline for Identification of ultrafilters with measures
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jul 27, 2018 at 1:36 | comment | added | mahdi meisami | @AndreasBlass By your first sentence maybe the second one is a better choice to search about it. | |
| Jul 26, 2018 at 20:31 | comment | added | Andreas Blass | An ultrafilter on any set $X$ amounts to a finitely additive $\{0,1\}$-valued measure on the power set of $X$. That is, what you wrote about $\mathbb N$ is true for all sets. I suspect, though, that you didn't really intend to ask about ultrafilters on arbitrary set but rather about points in the Stone-Cech compactification of arbitrary completely regular spaces. | |
| Jul 26, 2018 at 18:40 | comment | added | mahdi meisami | @MartinSleziak I am searching for a kind of method to achieve a measure from an ultrafilter or vice versa | |
| Jul 26, 2018 at 17:27 | comment | added | Martin Sleziak | I am not sure whether this is what you're looking for, but you have an isomorphism between $\ell_\infty$ and $C(\beta\mathbb N)$ and, consequently, isomorphism between the duals. This is also described in the Wikipedia article on Stone–Čech compactification. See also the answers here: The Duals of $l^\infty$ and $L^{\infty}$. | |
| Jul 26, 2018 at 17:11 | comment | added | mahdi meisami | @GeraldEdgar By what you said and searching that book in the case that our space is realcompact i.e. completely regular Hausdorff space with real elements of Stone-Chech compactificartion there is an identification. | |
| Jul 26, 2018 at 17:10 | history | edited | Martin Sleziak |
added (ultrafilters) tag
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| Jul 26, 2018 at 17:01 | history | edited | mahdi meisami | CC BY-SA 4.0 |
added 61 characters in body
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| Jul 26, 2018 at 16:59 | comment | added | mahdi meisami | I edited my question. We should speak about Stone-Chech compactification | |
| Jul 26, 2018 at 16:46 | comment | added | mahdi meisami | @GeraldEdgar what will be happen if we change to this: which conditions on Ston-Chech compatification of $X$ achieved from ultrafilter.? | |
| Jul 26, 2018 at 15:41 | comment | added | mahdi meisami | @GeraldEdgar Thanks for your suggestion | |
| Jul 26, 2018 at 15:40 | review | Close votes | |||
| Jul 28, 2018 at 14:41 | |||||
| Jul 26, 2018 at 15:40 | comment | added | Gerald Edgar | This great book that every student of analysis should read ... L. Gillman & M. Jerison, Rings of Continuous Functions | |
| Jul 26, 2018 at 15:34 | comment | added | mahdi meisami | @GeraldEdgar I have encountered with this question in reading of Vitaly Bergelson survey on Ergodic Ramsey theory during the process of defining Stone-Cech compactification. Where can i find what you said at the end of your comment?! | |
| Jul 26, 2018 at 15:26 | comment | added | Gerald Edgar | Needs more explanation. Does the definition of "ultrafilter" on a topological space have something to do with the topology? There is a measure characterization of realcompact spaces that may (or may not) be what you want here. | |
| Jul 26, 2018 at 15:23 | history | edited | mahdi meisami | CC BY-SA 4.0 |
edited title
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| Jul 26, 2018 at 15:17 | history | asked | mahdi meisami | CC BY-SA 4.0 |