Timeline for Topological properties of space of Radon measures
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2015 at 16:19 | comment | added | yada | Ok, Jordan-Hahn decomposition seems to be (sequentially) continuous (but clearly not injective). Thus, $M$ is at least Suslin and separable. | |
| Mar 19, 2015 at 15:33 | comment | added | yada | see Kallenberg, Random Measures, Appendix 15.7.7. He also refers to Bourbaki. The idea is to take a countable base $(C_k)_k$ of $\mathbb{R}$, approximate the indicator of $C_k$ by a sequence of functions $f_{ki}$ in $C_c$ and take $(f_{ki})_{k,i}$ as the countable set enumerated by $j$ to define a metric on $M$ by something like $\rho(\mu, \mu') := \sum_{j=1}^\infty \frac{1}{2^j} (1 - e^{-|\mu f_j - \mu' f_j|})$. | |
| Mar 19, 2015 at 15:27 | comment | added | Jochen Wengenroth | Did you try something with the Jordan-Hahn decomposition? For real-valued measures you would have a continuous surjection $M_+\times M_+ \to M$, $(\nu,\mu)\mapsto \nu-\mu$. | |
| Mar 19, 2015 at 15:25 | comment | added | Jochen Wengenroth | Why is the subset of positive measures polish? I believe that the set of probability measures is polish. | |
| Mar 19, 2015 at 11:03 | history | asked | yada | CC BY-SA 3.0 |