Timeline for Question regarding properties of map which produces measures that are invariant to orthogonal rotation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 3, 2022 at 6:52 | comment | added | Anthony Quas | Doesn't $\bar\pi$ send any rotationally-symmetric measure to itself? If so, it's immediate that $\bar\pi$ is surjective. | |
| Jul 2, 2022 at 19:45 | comment | added | Anthony Quas | My mistake. I somehow thought you were talking about the unit sphere. But in that case, aren’t measures completely described by the radial measure? | |
| Jul 1, 2022 at 16:11 | comment | added | Drew Brady | I don't think so. For instance a Gaussian truncated to the unit ball places much more mass near the origin than the Lebesgue (i.e., uniform) measure does, no? | |
| Jul 1, 2022 at 16:10 | comment | added | Anthony Quas | I think that’s also Lebesgue? | |
| Jul 1, 2022 at 15:50 | comment | added | Drew Brady | There are other measures, in general, which are rotation invariant, right? For instance, a (truncated) Gaussian with identity covariance. | |
| Jun 30, 2022 at 1:25 | comment | added | Anthony Quas | Isn’t Lebesgue measure the unique rotation-invariant measure up to scaling? If that’s so, the map $\bar\pi$ should be pretty easy to describe. | |
| Jun 29, 2022 at 22:46 | history | asked | Drew Brady | CC BY-SA 4.0 |