Timeline for Understanding a proof that the simplex of shift invariant probability measures on $\{0,1\}^\mathbb{Z}$ is Poulsen?
Current License: CC BY-SA 3.0
10 events
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| May 14, 2012 at 8:10 | vote | accept | user23644 | ||
| May 13, 2012 at 4:54 | answer | added | Vaughn Climenhaga | timeline score: 3 | |
| May 12, 2012 at 17:54 | comment | added | user23644 | @Vaughn I should add this argument interests me since it is so elementary and "natural": the measure is pushed onto the n consecutive coordinates, then the infinite tensor product is taken, and the result is averaged to become shift invariant. This is an instinctive approach to take, and it is rather disappointing that I can't follow it. | |
| May 12, 2012 at 17:42 | comment | added | user23644 | @Vaughn Yes, I have seen that question; I also know some other proofs of the fact, which I do understand. However, I am interested in this particular proof. | |
| May 12, 2012 at 17:37 | comment | added | user23644 | @Vaughn This is actually a collection of survey articles. Chapter 3 from which I cite the proof is written by G.H. Olsen. The full data from mathscinet is MR0565394 (81a:46004) Functional analysis: surveys and recent results. II. Proceedings of the Second Conference on Functional Analysis held at the University of Paderborn, Paderborn, January 31–February 4, 1979. Edited by Klaus-Dieter Bierstedt and Benno Fuchssteiner | |
| May 12, 2012 at 17:31 | history | edited | user23644 | CC BY-SA 3.0 |
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| May 12, 2012 at 16:21 | comment | added | Vaughn Climenhaga | It doesn't directly answer your specific question, but the fact that the simplex of invariant measures is Poulsen comes up (together with most of the proof) in the discussion on this other question: mathoverflow.net/questions/83981/… | |
| May 12, 2012 at 16:18 | comment | added | Vaughn Climenhaga | You mention that this is from a book, and you give the title - could you also give the author(s) to make the reference more complete? | |
| May 12, 2012 at 16:17 | comment | added | Vaughn Climenhaga | In your second paragraph, $\mu$ should be "a" shift-invariant measure, not "the" shift-invariant measure, since there are very many such measures | |
| May 12, 2012 at 15:25 | history | asked | user23644 | CC BY-SA 3.0 |