Timeline for "Strongly mutually singular" families of measures, and the set of ergodic measures
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2016 at 16:13 | comment | added | Julian Newman | Thank you! Alternatively: let $\mathcal{C} \subset \mathcal{B}(\mathbb{R})$ be a countable $\pi$-system generating $\mathcal{B}(\mathbb{R})$, and let $L(\mu)$ be the set of points $x$ such that for all $C \in \mathcal{C}$, $\frac{1}{n}\sum_{k=0}^{n-1}\mathbf{1}_C(f^k(x)) \to \mu(C)$. Measurable $A$-strong mutual singularity seems clear (using this same $L$); and moreover, since the sets $\{L(\mu):\mu \in \mathcal{S}\}$ are mutually disjoint, it should be easy to derive $B$-strong mutual singularity as a consequence. | |
| Aug 3, 2016 at 16:01 | vote | accept | Julian Newman | ||
| Aug 3, 2016 at 13:06 | history | edited | Ian Morris | CC BY-SA 3.0 |
added 862 characters in body
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| Aug 3, 2016 at 13:01 | history | edited | Ian Morris | CC BY-SA 3.0 |
added 862 characters in body
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| Aug 3, 2016 at 12:54 | history | answered | Ian Morris | CC BY-SA 3.0 |