Timeline for Alternate definitions of compact and weak mixing extensions
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2023 at 15:53 | comment | added | Uri Bader | Yes, this and the corollary that every pmp action is a weakly mixing extension of a tower of compact ones. | |
| Oct 6, 2023 at 15:50 | comment | added | Nate River | Thanks for the discussion so far. Do I understand correctly that by the Furstenberg structure theorem, you mean the one that says that every extension is either relatively weak mixing or has an intermediate relatively compact extension? Edit: Also yeah, I guess "intuitive" depends a lot on what your personal desired picture is. | |
| Oct 6, 2023 at 15:47 | comment | added | Uri Bader | @NateRiver, you asked "is there any equivalent formulation of relative weak mixing that is more immediately intuitive?" I guess this is rather subjective. | |
| Oct 6, 2023 at 15:45 | comment | added | Uri Bader | Ah, sure, this could be done. | |
| Oct 6, 2023 at 15:44 | comment | added | Nate River | Ah, I was thinking about the suggested repair by Terence Tao in the comments. | |
| Oct 6, 2023 at 15:42 | comment | added | Uri Bader | It is not pointless at all to formulate things measure theoretically. I would say that the usual definition of a weakly mixing extension is a measure theoretic one. However, I wouldn't call this a repair of your Definition 2... | |
| Oct 6, 2023 at 15:27 | comment | added | Nate River | Thank you for your alternative definition which I will go through shortly. Is it really pointless to try to formulate things measure theoretically though? It seems like Definition 2 can be repaired, though it may be asking too much for something similar for compact extensions… | |
| Oct 6, 2023 at 15:22 | history | answered | Uri Bader | CC BY-SA 4.0 |