Timeline for Dense sets in the space of continuous functions
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2011 at 15:02 | vote | accept | user17970 | ||
| Sep 21, 2011 at 15:02 | vote | accept | user17970 | ||
| Sep 21, 2011 at 15:02 | |||||
| Sep 20, 2011 at 22:25 | answer | added | George Lowther | timeline score: 12 | |
| Sep 20, 2011 at 20:59 | comment | added | George Lowther | ...ok, bounded above by one. Still no, with the example I just gave (the signed measure just has to have no atoms for $S$ to satisfy your property). | |
| Sep 20, 2011 at 20:57 | comment | added | George Lowther | Still no. Let $\mu$ be any finite signed measure on $[0,1]$ whose positive and negative parts $\mu^+,\mu^-$ have full support (nonzero measure on every nonempty open set). Then let $S\subseteq C([0,1])$ be the functions $f$ with $\int f\,d\mu=0$. | |
| Sep 20, 2011 at 20:55 | comment | added | user17970 | ... and bounded from above by $1$ | |
| Sep 20, 2011 at 20:54 | history | edited | user17970 | CC BY-SA 3.0 |
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| Sep 20, 2011 at 20:49 | comment | added | user17970 | Thanks George... I have corrected the question to demand that the functions in $S$ be positive. This is the situation I am really interested in. | |
| Sep 20, 2011 at 20:48 | history | edited | user17970 | CC BY-SA 3.0 |
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| Sep 20, 2011 at 20:42 | comment | added | George Lowther | No. For $X=[0,1]$, you can let $S$ be the set of functions with $\int\_0^1f(x)\,dx=0$. | |
| Sep 20, 2011 at 20:31 | history | asked | user17970 | CC BY-SA 3.0 |