Timeline for Can every ergodic map be approximated by ergodic maps close to the identity?
Current License: CC BY-SA 4.0
10 events
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| Apr 18, 2021 at 5:57 | history | bounty ended | CommunityBot | ||
| Apr 15, 2021 at 2:37 | comment | added | Nate River | Ah no, I definitely understand the use of “it’s obvious” in math usually isn’t to be condescending, but it’s more like “it’s obvious once you have the right point of view”, though the right point of view is usually not obvious or at least not trivial to obtain. Thanks for the solution again! | |
| Apr 15, 2021 at 2:30 | comment | added | Anthony Quas | By the way, re-reading what I wrote it sounds a bit condescending when I say “it’s obvious if you know Rokhlin...”). What I should have said is that there are a bunch of arguments of this flavor. If you know those, this argument feels familiar. | |
| Apr 12, 2021 at 3:48 | comment | added | Anthony Quas | If you don’t have a Lebesgue space, then something else that works is a countable set of measurable functions that separate points. Then $B_j$ is the set of points that are lexicographically minimal with when you obtain the vector of functions. | |
| Apr 11, 2021 at 14:08 | comment | added | Anthony Quas | Sorry Nate - I had in mind that the space is [0,1] as you say. This is not much of a restriction, but it isn't completely the general case. I'm not sure how you pick a "section" in the general case. Probably in any particular case it would be pretty easy. | |
| Apr 11, 2021 at 7:50 | vote | accept | Nate River | ||
| Apr 11, 2021 at 7:37 | comment | added | Nate River | (for instance $A_j=\{x\colon x=\min(x,Gx,\ldots,G^{j-1}x)\}$.) Sorry, what is the minimum over? Are you assuming some kind of measure conjugacy with [0, 1]? | |
| Apr 11, 2021 at 7:25 | comment | added | Nate River | This is surprising indeed, that any map close to the identity is the identity on a set of positive measure. I had heard of Rokhlin’s lemma but didn’t think much about its implications. | |
| Apr 11, 2021 at 6:57 | history | edited | Anthony Quas | CC BY-SA 4.0 |
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| Apr 11, 2021 at 6:36 | history | answered | Anthony Quas | CC BY-SA 4.0 |