Timeline for Is a bounded convex function $g$ that is non-negative on this particular convex set also non-negative on the its closure?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jan 5 at 7:11 | vote | accept | P. Quinton | ||
| Jan 5 at 6:52 | comment | added | P. Quinton | @usul any probability distribution that has smaller or larger tail than $p$ would be in $S\setminus T$, so for instance $q_n \propto \frac{p_n}n$. | |
| Jan 5 at 6:30 | comment | added | P. Quinton | @ChristianRemling Yes sorry, all "positive" should be "non-negative", I edited. | |
| Jan 5 at 6:29 | history | edited | P. Quinton | CC BY-SA 4.0 |
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| Jan 5 at 3:56 | answer | added | Anton Petrunin | timeline score: 2 | |
| Jan 5 at 2:21 | comment | added | usul | What is an example of a point in $S \setminus T$? | |
| Jan 4 at 21:00 | comment | added | Christian Remling | I think the question you ask in the title is not exactly the one asked in the text (this latter one has the trivial counterexample $g=0$, so the first one must be the one you wanted). | |
| Jan 4 at 18:02 | comment | added | Iosif Pinelis | You are right, $T$ is bigger than that. Somehow, I forgot that $A$ can be infinite. | |
| Jan 4 at 17:48 | comment | added | P. Quinton | @IosifPinelis Yes $A$ is nonempty, however I think that $T$ is actually larger than the convex hull of extreme points of $S$, indeed the extreme points are $e_i$ for all $i$ but $T$ can contain distribution with infinite support (like $p$). I am now rewording my attempt, thank you for the feedback. | |
| Jan 4 at 17:47 | comment | added | Iosif Pinelis | Also, I think your Attempts should carefully edited. | |
| Jan 4 at 17:46 | history | edited | P. Quinton | CC BY-SA 4.0 |
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| Jan 4 at 17:45 | comment | added | Iosif Pinelis | Also, $A$ should be required to be nonempty. Also, your $T$ is the convex hull of the set of all extreme points of $S$. | |
| Jan 4 at 17:44 | comment | added | P. Quinton | @IosifPinelis My bad, yes $g$ is convex and bounded on $S$ and non-negative on $T$. I edited accordingly. | |
| Jan 4 at 17:43 | history | edited | P. Quinton | CC BY-SA 4.0 |
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| Jan 4 at 17:14 | comment | added | Iosif Pinelis | Also, by "positive" do you actually mean "nonnegative"? | |
| Jan 4 at 16:57 | comment | added | Iosif Pinelis | Where is $g$ convex and bounded? On $S$ or only on $T$? | |
| Jan 4 at 14:48 | history | asked | P. Quinton | CC BY-SA 4.0 |