Timeline for An infinite-dimensional counterexample to a theorem of Lyapunov?
Current License: CC BY-SA 3.0
7 events
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| Mar 14, 2017 at 18:23 | comment | added | Christian Remling | This condition defines a (weak $*$) dense subset, so one can now just pick measures $\mu_{n,k}$ that (as $k\to\infty$) approach the measures $\mu_n$ from Anthony's original counterexample. Since $\mu_{n,k}(A)$ will be close $\mu_n(A)$ for large $k$ for any clopen $A$, this is still a counterexample to your conjecture. | |
| Mar 14, 2017 at 9:50 | comment | added | Julien Melleray | I'm sorry, but I don't understand your comment: certainly, the condition that all measures in the closure of $(\mu_i)$ are nonatomic and with full support is a nontrivial addition to the fact that each $\mu_i$ satisfies those conditions. So, I am not sure what you mean? | |
| Mar 13, 2017 at 20:56 | comment | added | Christian Remling | For a clopen set $A$ you have that $\mu(A)=\lim \mu_n(A)$ if $\mu_n\to\mu$ in weak-$*$ sense, so no set of extra conditions that still leaves you with a dense set of measures can change anything. | |
| Mar 13, 2017 at 8:45 | history | edited | Julien Melleray | CC BY-SA 3.0 |
Added an updated question below the original one.
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| Mar 13, 2017 at 8:12 | vote | accept | Julien Melleray | ||
| Mar 12, 2017 at 22:56 | answer | added | Anthony Quas | timeline score: 2 | |
| Mar 12, 2017 at 21:19 | history | asked | Julien Melleray | CC BY-SA 3.0 |