Timeline for Non-absolutely continuous foliation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2023 at 17:55 | vote | accept | RegularGraph | ||
| Sep 10, 2023 at 17:54 | comment | added | RegularGraph | @DanielAsimov Thanks, this is exactly the type of thing I was hoping for, should have thought of it myself! And, it's nice that the individual leaves are lines, as nice a curve as one could hope for. | |
| Sep 10, 2023 at 1:46 | history | became hot network question | |||
| Sep 10, 2023 at 0:39 | comment | added | Vaughn Climenhaga | Indeed, one can accomplish this, but the foliation in Hasselblatt-Katok, and the one in Milnor's article, exhibit an even more pathological property; see the edit to my answer. | |
| Sep 9, 2023 at 19:58 | comment | added | Daniel Asimov | Since a) all (topological) Cantor sets embedded in ℝ are equivalent to each other by a homeomorphism of ℝ, and b) a Cantor set in ℝ can have either 0 or positive Lebesgue measure, it follows that one can construct a (topological) foliation F of the torus by curves such that F is not absolutely continuous. | |
| Sep 9, 2023 at 16:20 | answer | added | Vaughn Climenhaga | timeline score: 4 | |
| Sep 9, 2023 at 14:17 | history | asked | RegularGraph | CC BY-SA 4.0 |