Timeline for Separable sigma-algebra: equivalence of two definitions
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 14 at 16:37 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor formatting (embedded link)
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| Feb 23, 2017 at 18:01 | comment | added | Julian Newman | As this is an important question I just want to summarise the key points from the different answers below: $(X,\mathcal{S},\mu)$ is a measure space. (I) The semi-metric $\mu(A \triangle B)$ is separable if and only if $\exists$ countable set $\mathcal{S}_0 \subset \mathcal{S}$ s.t. $\mathcal{S} \subset \sigma(\mathcal{S}_0 \cup \mathcal{N}_\mu)$. (II) It is possible that the semi-metric $\mu(A \triangle B)$ is separable but there is no countable set $\mathcal{S}_0 \subset \mathcal{S}$ s.t. $\mathcal{S} \subset \sigma(\mathcal{S}_0 \cup \mathcal{N}_{\mu|_{\sigma(\mathcal{S}_0})})$. | |
| May 28, 2012 at 20:46 | answer | added | Vaughn Climenhaga | timeline score: 9 | |
| Jun 9, 2010 at 8:40 | vote | accept | Kestutis Cesnavicius | ||
| Jun 9, 2010 at 2:31 | comment | added | Joel David Hamkins | Kestutis, I explain how to do this in my updated answer. You can use the finite Boolean combinations of the generating set. | |
| Jun 8, 2010 at 21:07 | comment | added | Kestutis Cesnavicius | Say the $\sigma$-algebra is countably generated. How do I pick the countable dense subset in the semi-metric given by $\mu(A\Delta B)$? | |
| Jun 8, 2010 at 19:25 | answer | added | coudy | timeline score: 10 | |
| Jun 8, 2010 at 19:19 | answer | added | Joel David Hamkins | timeline score: 15 | |
| Jun 8, 2010 at 19:16 | comment | added | Nate Eldredge | I'm too lazy to try to prove this right now, but where does your proof get stuck? | |
| Jun 8, 2010 at 18:43 | comment | added | François G. Dorais | For convenience, I copied the Wikipedia article in a community wiki answer. | |
| Jun 8, 2010 at 18:42 | answer | added | François G. Dorais | timeline score: 4 | |
| Jun 8, 2010 at 18:18 | history | asked | Kestutis Cesnavicius | CC BY-SA 2.5 |