Timeline for Closure of polynomials of a function in $L^2$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2018 at 9:01 | vote | accept | Tommi | ||
| Feb 14, 2018 at 18:47 | answer | added | Nate Eldredge | timeline score: 6 | |
| Feb 14, 2018 at 16:53 | comment | added | Nate Eldredge | Stone-Weierstrass says that if $f$ is continuous and injective, then $P_f$ is uniformly dense in $C(I)$, which implies it is dense in $L^2$. More generally, I think a necessary and sufficient condition would be that the $\sigma$-algebra $\sigma(f) = \sigma(f^{-1}(B) : B \in \mathcal{B}_{\mathbb{R}})$ contains the Borel $\sigma$-algebra of $I$ in its completion. I think we can prove this with the Dynkin multiplicative system lemma. I will try to flesh it out later if I get a chance. | |
| Feb 14, 2018 at 14:21 | history | edited | Tommi | CC BY-SA 3.0 |
added an example and a tag
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| Feb 14, 2018 at 13:55 | comment | added | Jochen Wengenroth | Perhaps this question mathoverflow.net/questions/96006/… has some relevance? | |
| Feb 14, 2018 at 13:47 | history | edited | Tommi | CC BY-SA 3.0 |
added 142 characters in body
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| Feb 14, 2018 at 13:38 | history | asked | Tommi | CC BY-SA 3.0 |