Timeline for Convergence in $\mathbb{L}_1$ implies convergence "perturbed" conditional expectations
Current License: CC BY-SA 4.0
15 events
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| Jul 16 at 14:48 | answer | added | unwissen | timeline score: 1 | |
| Jul 16 at 14:40 | history | edited | Grandes Jorasses | CC BY-SA 4.0 |
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| Jul 16 at 14:40 | history | undeleted | Grandes Jorasses | ||
| Jul 16 at 14:40 | history | deleted | Grandes Jorasses | via Vote | |
| Jul 16 at 8:25 | comment | added | unwissen | Okay, and what measure do you have on $Y$? Are your "Polish spaces" just $\mathbb{R}$? It's a little bit tiring to ask for all that things which cannot be guessed from context. I suggest that you try to make the question understandable without having to ask so much, as I and probably others want to help but not worm everything out of you.. | |
| Jul 16 at 7:40 | comment | added | Grandes Jorasses | no the $\epsilon$-$L_1$-neighborhoods of a density $f_0$ are defined with respect to any measure $\nu$ with $supp(\nu) \subset X$ as follows: $$ \bigg\{ f : \int \| f( \cdot | x) - f_0( \cdot | x)\|_1 d \nu(x) < \epsilon \bigg\}$$ In the above mentioned case, the measure $\nu$ can be assumed to be the true measure according to which the $X$ are distributed. It can be also assumed it has a density $v(x)$, bounded away from 0 and infinity | |
| Jul 16 at 7:25 | comment | added | unwissen | Okay. So the $L^1$-convergence is meant just with right to $y$? What is the corresponding measure? Then why does your "perturbed" term not depend on $y$? | |
| Jul 16 at 7:04 | comment | added | Grandes Jorasses | I also wrote it now in a more precise way so that it is clear that I meant the densities of normals | |
| Jul 16 at 7:03 | history | edited | Grandes Jorasses | CC BY-SA 4.0 |
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| Jul 16 at 6:51 | comment | added | unwissen | It is better now, but I must say that I still don't understand the exact question. Is $X$ random? Why does nothing depend on $y$? Do you mean the density of the corresponding normal distribution by $N$? | |
| Jul 16 at 6:39 | history | edited | Grandes Jorasses | CC BY-SA 4.0 |
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| Jul 16 at 6:24 | comment | added | Grandes Jorasses | I added this corrections | |
| Jul 16 at 6:23 | history | edited | Grandes Jorasses | CC BY-SA 4.0 |
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| Jul 15 at 21:56 | comment | added | unwissen | The question as it stands is not understandable at all for me. What do all of the symbols mean? Somehow the LHS doesn't even depend on $n$? What is $\omega_k(X)$? What do you really mean by $N(\dots, \dots)$? | |
| Jul 15 at 21:06 | history | asked | Grandes Jorasses | CC BY-SA 4.0 |