Timeline for A question on unit norm elements of $\ell^2 \setminus \bigcup_{0<p<2 }\ell^p$
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Aug 19 at 13:37 | comment | added | Bill Johnson | The book is in the list on Wikipedia: Geometric nonlinear functional analysis (with Yoav Benyamini). Colloquium publications, 48. American Mathematical Society, 2000. | |
| Aug 18 at 10:44 | comment | added | Ali Taghavi | en.wikipedia.org/wiki/Joram_Lindenstrauss | |
| Aug 18 at 10:44 | comment | added | Ali Taghavi | @BillJohnson BTW what was the title of the book you mentioned? I did not find a book in this list of the following wikipedia coauthored by Benyamini | |
| S Aug 18 at 10:10 | history | suggested | J. W. Tanner | CC BY-SA 4.0 |
Improved English / formatting
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| Aug 18 at 9:56 | comment | added | Ali Taghavi | @BillJohnson What can be said about the topological or Hausdorff dimension of A and its complement? | |
| Aug 18 at 2:43 | review | Suggested edits | |||
| S Aug 18 at 10:10 | |||||
| Aug 17 at 16:33 | comment | added | Ali Taghavi | @BillJohnson Thank you very much Prof. Johnson for your attention | |
| Aug 17 at 15:57 | comment | added | Bill Johnson | For your second question, read Chapter 6 in the book of Benyamini and Lindenstrauss for concepts of null sets and their uses. | |
| Aug 17 at 13:01 | answer | added | Aleksei Kulikov | timeline score: 4 | |
| Aug 17 at 11:27 | answer | added | David Gao | timeline score: 2 | |
| Aug 17 at 10:47 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
added 231 characters in body
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| Aug 17 at 10:37 | comment | added | Ali Taghavi | @DavidGao Ok I add a link of density to note. | |
| Aug 17 at 10:34 | comment | added | David Gao | Ah, I see what you meant. You should probably clarify that in the question. (Or just remove the note altogether if it’s not important anyway.) It is a bit confusing as it seems like you’re asking whether $A$ is dense. | |
| Aug 17 at 10:34 | comment | added | Ali Taghavi | @DavidGao This is the reason that I did not include the Note part into the main question. If I have an obvious measure then I would ask what can be said about the measure of A or its complement | |
| Aug 17 at 10:32 | comment | added | Ali Taghavi | So I would need to a kind of measure! | |
| Aug 17 at 10:31 | comment | added | Ali Taghavi | @DavidGao Oh I get what you say. By density I meant some thing as follows: Let A is a subset of of topological measur space the density of A at a point p is the limit $\frac{\mu (A\cap U)}{\mu(U)}$ where U shrink to p among open neighborhoods of p | |
| Aug 17 at 10:28 | comment | added | Ali Taghavi | @DavidGao No the density is obvious but the 2 items I mentioned is my main questions. | |
| Aug 17 at 10:25 | comment | added | David Gao | I thought your note meant you’re thinking about asking whether $A$ is dense? I suppose I was mistaken. | |
| Aug 17 at 10:21 | comment | added | Ali Taghavi | @DavidGao Obviously both $A$ and $S\setminus A$ are dense. I do not get what do you meant? | |
| Aug 17 at 10:17 | comment | added | David Gao | $A$ is dense, also by Baire category. (Or, really, it’s just the unit sphere minus a proper subspace. Of course it’s dense.) | |
| Aug 17 at 10:10 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
edited body
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| Aug 17 at 9:54 | history | asked | Ali Taghavi | CC BY-SA 4.0 |