Timeline for Ergodicity with respect to the shift
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2013 at 2:03 | vote | accept | Umberto | ||
| Feb 12, 2013 at 22:34 | comment | added | Anthony Quas | It seems from this and your previous post that you have some wrong idea in mind of the notion of ergodic. To give a really simple example (the simplest of Vaughn's examples below), imagine a measure supported at the point 0000...... That is $\mu(A)$ is 1 if $A$ contains $000\ldots$ and 0 otherwise. It's not hard to check that $\mu$ is invariant: $A$ contains $0\ldots$, if and only if $S^{-1}A$ contains $0\ldots$. It's also immediate that $\mu$ is ergodic. You have to show that every invariant set has measure 0 or 1. -- But every set has measure 0 or 1. | |
| Feb 12, 2013 at 21:10 | answer | added | Vaughn Climenhaga | timeline score: 6 | |
| Feb 12, 2013 at 21:02 | history | asked | Umberto | CC BY-SA 3.0 |