Timeline for Convergence of sets
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2011 at 8:27 | vote | accept | SBF | ||
| Jan 23, 2011 at 21:21 | comment | added | SBF | I've just mentioned that I forgot to write that the sequence $A_n$ is non-increasing. Since the limit is understood as a set which belongs to all $A_n$. | |
| Jan 23, 2011 at 21:20 | history | edited | SBF | CC BY-SA 2.5 |
added 47 characters in body
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| Jan 23, 2011 at 21:06 | answer | added | Did | timeline score: 1 | |
| Jan 23, 2011 at 17:24 | comment | added | Anthony Quas | Could you make the question more precise? From the hypothesis it seems that taking $A_n=E$ for all $n$ would satisfy the condition. Also what do you mean by a limit set? In the Hausdorff metric? the set of points that belong to all $A_n$ for $n$ greater than some $n_0$? Also what is $A_0$? What I think this might mean is this: think of $\phi$ as the transition kernel for a MC. Let $A_0=E$; Let $A_1$ be the support of the random variable $X_1$ given that $X_0$ has some distribution with support $E$. Now let $A_2$ be the support of $X_2$ etc. Is this right? | |
| Jan 23, 2011 at 13:34 | comment | added | fedja | What do you mean by "Since $A_n$ are compacts, there is a limit $A=\lim_n A_n$"? The set of compact sets is by no means compact itself. | |
| Jan 23, 2011 at 13:20 | history | asked | SBF | CC BY-SA 2.5 |