Timeline for Commuting supremum and expectation
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Jan 13, 2023 at 17:45 | comment | added | ABIM | @Did Was an answer on this ever settled? | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 19, 2011 at 10:42 | comment | added | Did | @zhoraster: Not interested in answering the question in my comment? Let me recall it: in the first line of your answer, why should $M$ be measurable? | |
| Jun 19, 2011 at 10:40 | comment | added | Did | @Johannes: Not interested in answering the question in my comment? Let me recall it: why should $M$ be measurable? | |
| Feb 15, 2011 at 13:27 | comment | added | Did | .../... Assume for instance that $\Omega\subseteq U$ and fix $V\subset\Omega$. Define the family $(X_a)$ by $X_a(\omega)=1$ if $a\in V$ and $\omega=a$, and $X_a(\omega)=0$ otherwise. Then $M(\omega)=1$ if $\omega\in V$ and $M(\omega)=0$ otherwise, hence $M=\mathbf{1}_V$ and, since $V$ can be any subset of $\Omega$, it may well happen that $M:(\Omega,\mathcal{F})\to(\mathbb{R},\mathcal{B}(\mathbb{R}))$ is not measurable. If you could explain what I miss, I would be grateful. | |
| Feb 15, 2011 at 13:27 | comment | added | Did | @Johannes @zhoraster Sorry to be late at the party but I am afraid I do not understand what is going on. Let me stick to the (apparently) definitive version of Johannes' post, above this comment. One starts with $U\subseteq \mathbb{R}$ and with a family $(X_a)$ of real valued random variables $X_a:(\Omega,\mathcal{F})\to(\mathbb{R},\mathcal{B}(\mathbb{R}))$, indexed by $a\in U$, and one introduces $M=\sup_{a\in U}X_a$. I wonder why $M$ should be measurable in the first place, clearly or not. :-) .../... | |
| Dec 8, 2010 at 10:38 | comment | added | zhoraster | Looks good, I don't see a mistake. | |
| Dec 8, 2010 at 8:19 | vote | accept | Johannes | ||
| Dec 5, 2010 at 13:07 | vote | accept | Johannes | ||
| Dec 5, 2010 at 13:07 | |||||
| Dec 4, 2010 at 16:50 | history | edited | Johannes | CC BY-SA 2.5 |
added 134 characters in body
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| Dec 4, 2010 at 16:37 | history | edited | Johannes | CC BY-SA 2.5 |
clearify the question and summerize the given answers; added 10 characters in body; added 2 characters in body
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| Dec 4, 2010 at 16:28 | history | edited | Johannes | CC BY-SA 2.5 |
deleted 3 characters in body; edited title; Post Made Community Wiki
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| Dec 3, 2010 at 19:19 | answer | added | zhoraster | timeline score: 4 | |
| Dec 2, 2010 at 13:52 | answer | added | FraoncoisL | timeline score: -1 | |
| Dec 2, 2010 at 9:37 | history | edited | Johannes | CC BY-SA 2.5 |
deleted 114 characters in body
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| Dec 2, 2010 at 8:45 | history | asked | Johannes | CC BY-SA 2.5 |