Timeline for Sigma-algebras on Banach Spaces.
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Mar 22, 2011 at 13:56 | comment | added | Ravil Mudarisov | Thanks a lot. About l∞ we should use open ball of radius 1, and i think to show that it is neither cylindrical set nor can not be represented as intersection of cylinders. | |
| Mar 22, 2011 at 13:39 | comment | added | Gerald Edgar | Set $[0,1/2]^{[0,1]}$ does not depend on only countably many coordinates, so it is not Baire. These are comments rather than answers, since they are not about $l^\infty$. | |
| Mar 22, 2011 at 8:15 | history | edited | Ravil Mudarisov | CC BY-SA 2.5 |
deleted 16 characters in body
|
| Mar 22, 2011 at 5:07 | comment | added | Ravil Mudarisov | But why [0,1/2]^{[0,1]} is not baire? And what about l-infinitive? | |
| Mar 21, 2011 at 23:54 | comment | added | Gerald Edgar | Correct, a singleton is a closed set, therefore Borel. Also, the more complicated set $[0,1/2]^{[0,1]}$ is closed, therefore Borel. | |
| Mar 21, 2011 at 20:07 | comment | added | Ravil Mudarisov | And i think of the set {0}. | |
| Mar 21, 2011 at 19:55 | comment | added | Ravil Mudarisov | "The product sigma-algebra has the property that every set in it depends on only countably many coordinates." - that is from defenition of Baire sigma-algebra on product spaces, am I right? | |
| Mar 21, 2011 at 19:42 | comment | added | Ravil Mudarisov | Ok, they are not equal. It would be great if there is example of Borel, not Baire(Cylindrical) set. I think of [0,1/2]^{[0,1]}, but didnt prove it yet. Maybe you can give me other examples? | |
| Mar 21, 2011 at 18:29 | comment | added | Gerald Edgar | And $[0,1]^{[0,1]}$ is interesting for the sigma-algebra, too. The product sigma-algebra (= the Baire sigma-algebra) has the property that every set in it depends on only countably many coordinates. In particular, a singleton is NOT in this sigma-algebra. So the Baire sigma-algebra is not the same as the Borel sigma-algebra. | |
| Mar 21, 2011 at 17:00 | comment | added | Nate Eldredge | $[0,1]^{[0,1]}$ (with the product topology) is not metrizable. | |
| Mar 21, 2011 at 16:31 | history | edited | Ravil Mudarisov |
edited tags
|
|
| Mar 21, 2011 at 16:07 | history | asked | Ravil Mudarisov | CC BY-SA 2.5 |