Timeline for Is a measurable homomorphism on a Lie group smooth?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2013 at 17:44 | vote | accept | Tom LaGatta | ||
| Feb 5, 2013 at 18:07 | comment | added | Tom LaGatta | And André Henriques provides the very nice intuition: mathoverflow.net/questions/64116/… | |
| Feb 5, 2013 at 18:06 | comment | added | Tom LaGatta | Excellent, I just looked at your other question. Alain Varette provides a nice reference to Adam Kleppner's paper. A measurable homomorphism of locally compact groups is continuous. Since Lie groups are locally compact, this proves it. Direct link to Alain Varette's answer: mathoverflow.net/questions/64116/… | |
| Feb 5, 2013 at 18:04 | comment | added | Tom LaGatta | Thanks @Marc Palm. I meant homomorphism but I foolishly neglected to say it. Why is the answer yes in general? Intuitively, the Borel $\sigma$-algebra contains all the topological information of the space, hence the differential information since $G$ is a Lie group. However, this is just heuristic speculation and I don't know a good argument which makes this fact apparent. | |
| Feb 4, 2013 at 13:19 | comment | added | Marc Palm | The counterexample works if X is not open. Taking X as the connected component of the identity wouldn't work. | |
| Feb 4, 2013 at 13:14 | history | edited | Marc Palm | CC BY-SA 3.0 |
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| Feb 4, 2013 at 9:32 | comment | added | Marc Palm | See here for example: mathoverflow.net/questions/64116/… | |
| Feb 4, 2013 at 9:30 | history | answered | Marc Palm | CC BY-SA 3.0 |