Timeline for If $f_k \not\to 0$ a.e., does there exist a subsequence, a set of positive measure, and $c > 0$, on which $\liminf |f_{k_j}| > c$?
Current License: CC BY-SA 3.0
10 events
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| S Aug 3, 2013 at 5:39 | history | edited | Misha | CC BY-SA 3.0 |
Latexed math in title to make it readable.
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| S Aug 3, 2013 at 5:39 | history | suggested | Michael Albanese | CC BY-SA 3.0 |
Latexed math in title to make it readable.
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| Aug 3, 2013 at 5:29 | review | Suggested edits | |||
| Aug 3, 2013 at 5:39 | |||||
| Jul 20, 2010 at 18:54 | comment | added | Mykie | Convergence a.e. does not imply convergence in measure. Consider f_{n} defined as f_{n}(x)=1 x>n and f_{n}(x)=0 x<=n. | |
| Jul 4, 2010 at 16:35 | vote | accept | Nicolò | ||
| Apr 5, 2010 at 15:14 | comment | added | Nicolò | Thanks for your comment. I know that convergence in measure does not imply a.e. convergence (I use Folland's Real Analysis, and there there is a good section on convergence in measure), but my question was more about the inverse, I think. | |
| Apr 4, 2010 at 18:35 | comment | added | Gerald Edgar | Your measure theory textbook surely has a discussion of this. Perhaps called "convergence in measure". The "no" answer below shows that convergence in measure does not imply a.e. convergence. This same example is probably in your textbook. | |
| Apr 4, 2010 at 16:42 | answer | added | Nicolò | timeline score: 3 | |
| Apr 4, 2010 at 16:34 | history | edited | Nicolò | CC BY-SA 2.5 |
deleted 17 characters in body
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| Apr 4, 2010 at 16:24 | history | asked | Nicolò | CC BY-SA 2.5 |