Timeline for Is the following sequence convergent in the weak topology?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2017 at 18:52 | vote | accept | g.pomegranate | ||
| Feb 11, 2017 at 18:16 | answer | added | Nate Eldredge | timeline score: 1 | |
| Feb 11, 2017 at 18:03 | comment | added | g.pomegranate | I want to verify if there is a measure $\mu^*$ such that $$(f, \mu_n) \to (f, \mu^*),$$ for $f$ bounded and continuous, where $(f, \mu)$ means $\int f d\mu$. | |
| Feb 11, 2017 at 17:59 | comment | added | Nate Eldredge | "Weak topology" in this context means different things to probabilists and analysts, so can you please state precisely which topology is meant? | |
| Feb 11, 2017 at 17:57 | comment | added | g.pomegranate | I don't understand. Can you give me more details, please? Thank you! | |
| Feb 11, 2017 at 17:42 | comment | added | Nate Eldredge | Hint: If $\mu_n$ is the measure you defined, can you show that $$\int f\,d\mu_n = \frac{1}{\tau_n} \int_0^{\tau_n} \int_{\mathbb{R}} f(x + t)\,\mu(dx)\,dt$$ for bounded continuous $f$? Then try Fubini and dominated convergence. | |
| Feb 11, 2017 at 17:38 | history | edited | g.pomegranate | CC BY-SA 3.0 |
deleted 60 characters in body
|
| Feb 11, 2017 at 17:30 | history | asked | g.pomegranate | CC BY-SA 3.0 |