Timeline for Heine-Borel property for (probability) measures on $\mathcal{S}'$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 29 at 13:25 | comment | added | Isaac | @unwissen Thank you very much for reminding me of the keywords I forgot some time ago! | |
| Jun 29 at 13:16 | comment | added | unwissen | To be honest, I'm not an expert on this and just wanted to know why you didn't mention the (for Polish spaces very standard) "tightness method" in your question, but my internet search brought me to arxiv.org/abs/1706.09326, where maybe Corollary 2.4 and the reference right before Lemma 5.2 may be of interest. | |
| Jun 29 at 12:55 | comment | added | Isaac | @unwissen By strong topology on $\mathcal{S}'$, you mean the strong dual topology? Anyway...I do recall running into the notion of tightness before...perhaps could you recommend any reference relevant for $\mathcal{S}'$? | |
| Jun 29 at 11:08 | comment | added | unwissen | This doesn't answer your precise question, but tightness of $(\mu_n)_n$ (i.e. for all $\epsilon > 0$ there is a compact (in the weak (!) topology; so for example the Banach-Alaoglu theorem can provide this) set $K_\epsilon$ such that $\sup_n \mu_n(K_\epsilon) \geq 1-\epsilon$) would be a sufficient condition to extract a convergent (where convergence here means convergence in distribution where one tests against bounded functions $\mathcal{S}' \to \mathbb{R}$ which are continuous when $\mathcal{S}'$ is equipped with the strong (!) topology) subsequence, no? | |
| Jun 28 at 22:21 | history | asked | Isaac | CC BY-SA 4.0 |