Timeline for Convergence of probability measures on a generating field of a sigma-field
Current License: CC BY-SA 3.0
3 events
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| Sep 20, 2012 at 4:55 | comment | added | Wei Mao | I don't see in your example for what event $F$ $m_n(F)\to m(F)$ is false. A "standard field" is a term in R. Gray's book Probability, Random Processes, and Ergodic Properties. A field is standard if it possesses a basis, which is a sequence of finite fields $\mathcal{F}_n$ with the following properties: 1. $\mathcal{F}_n$ asymptotically generates F, that is, $\mathcal{F}_n\subset\mathcal{F}_{n+1}$ and $\mathcal{F} = \bigcup_n\mathcal{F}_n$. 2. If $G_n$ is a sequence of atoms of $\mathcal{F}_n$ such that $G_{n+1}\subset G_n$, then $\bigcup_n G_n\neq\emptyset$. | |
| Sep 19, 2012 at 23:51 | comment | added | George Lowther | No, you can have measures whose supports are finite sets tending towards (atomless) measures. E.g., the average over n equally spaced points tends the uniform distribution (I have cantor space in mind here). But, I am not familar with the term "standard generating field". What kind of examples do you have in mind? | |
| Sep 19, 2012 at 18:09 | history | asked | Wei Mao | CC BY-SA 3.0 |