Timeline for A property of measures on a Polish space
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22, 2022 at 19:27 | vote | accept | Ibra | ||
| Sep 22, 2022 at 18:05 | answer | added | Dominik Kutek | timeline score: 1 | |
| Sep 22, 2022 at 17:47 | comment | added | Ibra | I honestly could not conclude. Application of monotone class theorem requires the set of Balls to be stable by intersection which is not the case. I don't know whether I can proceed differently. Thanks! | |
| Sep 22, 2022 at 16:19 | comment | added | Dominik Kutek | So I would suggest defining $\phi_{k,n} = 1_{B(x_k,\frac{1}{n})}$. Then $\int_Y \phi_{k,n}d\nu_1 = \int_{Y}\phi_{k,n} d\nu_2$ means $\nu_1(B(x_k,\frac{1}{n})) = \nu_2(B(x_k,\frac{1}{n}))$. Try to show that this implies $\nu_1(U) = \nu_2(U)$ for any open set $U$. | |
| Sep 22, 2022 at 16:15 | comment | added | Ibra | Yes, I know a similar result | |
| Sep 22, 2022 at 16:08 | comment | added | Dominik Kutek | Do you know, that any open set in a separable metric space can be written as countable union of open balls? Precisely, if $\{x_k\}_k$ is a countable dense subset in $Y$, then any open set $U$ can be written as $U = \bigcup_{x_k \in U, n \in \mathbb N} B(x_k,\frac{1}{n})$, where $B(x_k,\frac{1}{n})$ is an open ball centered at $x_k$ with radius $\frac{1}{n}$. | |
| Sep 22, 2022 at 16:04 | comment | added | Ibra | Sorry for my lack of precision. It is indeed the Borel sigma-field. | |
| Sep 22, 2022 at 15:34 | comment | added | Dominik Kutek | Is $\mathcal Y$ arbitrary $\sigma-$field on $Y$, or Borel $\sigma-$field? | |
| Sep 22, 2022 at 15:14 | history | edited | Ibra | CC BY-SA 4.0 |
edited title
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| Sep 22, 2022 at 14:59 | history | asked | Ibra | CC BY-SA 4.0 |