Timeline for Ergodic limits along subsets of $\mathbb{N}.$
Current License: CC BY-SA 3.0
21 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 1, 2015 at 22:07 | history | edited | Pietro Majer | CC BY-SA 3.0 |
minor edit
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| Sep 29, 2013 at 15:03 | history | edited | Ricardo Andrade |
added top level tag
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| Sep 29, 2013 at 10:08 | history | edited | Pietro Majer | CC BY-SA 3.0 |
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| Nov 1, 2010 at 15:37 | vote | accept | Pietro Majer | ||
| Oct 24, 2010 at 18:49 | answer | added | coudy | timeline score: 9 | |
| Oct 24, 2010 at 18:42 | answer | added | Mark | timeline score: 4 | |
| Oct 24, 2010 at 16:59 | answer | added | Gerald Edgar | timeline score: 2 | |
| Oct 24, 2010 at 14:59 | comment | added | Pietro Majer | Actually, your clarifying example generalize to show that a set $mA$ is never "nice" if $m>1.$ Maybe there's a characterization of "nice" sets in terms of their relative distribution within arithmetic progression; like primes according to Dirichlet theorem. | |
| Oct 24, 2010 at 11:48 | comment | added | Pietro Majer | Thank you, I see, you are right. Maybe a more natural definition is, removing any ergodicity assumption and just ask for convergence a.e. to the conditional expectation w.r.to the $T$-invariant sets, $\mathbb{E}(f|\Sigma_T).$ Even so, the operation $m\to m A$ seems a dangerous one. | |
| Oct 24, 2010 at 11:44 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Oct 24, 2010 at 3:49 | comment | added | Ori Gurel-Gurevich | if the measure is uniform on {0,1} then the transformation T swapping 0 and 1 is ergodic, but $T^2$ isn't, so according to your definition $2\mathbb{N} isn't nice. Or maybe I misunderstood something? | |
| Oct 23, 2010 at 21:10 | comment | added | Pietro Majer | @Ori: sorry, I can't see why... What's the problem with atoms? | |
| Oct 23, 2010 at 18:56 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Oct 23, 2010 at 17:28 | comment | added | Ori Gurel-Gurevich | It is not true that $mA$ is nice, unless you restrict your space to non-atomic ones... | |
| Oct 23, 2010 at 17:03 | comment | added | Pietro Majer | And slightly more generally, if $|A\Delta B\cap [0,x)|=o(|A\cap [0,x)|)$ as $x\to\infty .$ | |
| Oct 23, 2010 at 16:15 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Oct 23, 2010 at 15:43 | comment | added | Kevin O'Bryant | If $A$ is nice, and the symmetric difference of $A,B$ is finite, then $B$ is nice. | |
| Oct 23, 2010 at 15:42 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Oct 23, 2010 at 14:58 | history | edited | Pietro Majer | CC BY-SA 2.5 |
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| Oct 23, 2010 at 14:38 | history | asked | Pietro Majer | CC BY-SA 2.5 |