Timeline for Energy in doubling measure metric spaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2018 at 11:22 | answer | added | Stefano Gogioso | timeline score: 1 | |
| Aug 31, 2018 at 3:48 | comment | added | BigM | Let's rule that out. Id rather to find counterexamples for non atomic measures and also none discrete . | |
| Aug 31, 2018 at 2:09 | comment | added | Christian Remling | $X=\{ x\}$ gives such examples. | |
| Aug 30, 2018 at 20:52 | comment | added | BigM | In fact, for some nice Riemannian manifold our double integral is bounded. My limited personal experience suggests its bounded for general care. | |
| Aug 30, 2018 at 20:41 | comment | added | Aryeh Kontorovich | Ah ok thanks. I somehow only thought the large values of $d(x,y)$ could be problematic -- ignored the small ones. | |
| Aug 30, 2018 at 20:16 | comment | added | BigM | No.it doesnt.d(x,y) can be very small , consequently log^2 can be very large. In many cases integal becomes bounded but even in R^n it's not obvious, at least to me, why for an arbitrary measure the double integral should be bounded. it's trivial that its bounded bellow though. :) | |
| Aug 30, 2018 at 20:07 | comment | added | Aryeh Kontorovich | If $U$ is compact, then in particular it's bounded and so $d(x,y)$ is upper-bounded by some $M<\infty$. Doesn't that make the integral trivially finite? | |
| Aug 30, 2018 at 17:20 | history | asked | BigM | CC BY-SA 4.0 |