Timeline for Do you know important theorems that remain unknown?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 26, 2019 at 17:51 | comment | added | coudy | @Sinusx $f$ is not assumed to be integrable. | |
| Feb 22, 2019 at 23:43 | comment | added | Viktor B | Isn't it a consequence of the dominated convergence theorem? | |
| Jul 26, 2018 at 18:01 | comment | added | coudy | @YemonChoi Indeed, thanks for pointing the correct reference. | |
| Jul 23, 2018 at 4:26 | comment | added | Yemon Choi | Are you sure Joel's article was in the AMM? According to arxiv.org/abs/1412.7702 it was published in the Irish Mathematical Society's Bulletin | |
| Jun 5, 2018 at 19:08 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 7 characters in body
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| May 1, 2018 at 16:20 | comment | added | BCLC | @lcv DCT has integrable $g$ rather than nonnegative $f$ right? | |
| Apr 25, 2018 at 16:11 | comment | added | Ovi | I am an undergrad just familiar with the Lebesgue measure, not with measure spaces. I am surprised that about your example; I haven't had time to digest it, but I was under the impression that the D.C.T. and Fatou;s lemma imply the result in your post. If $f$ is integrable, then it is a dominating function and D.C.T applies. If not, then $\int f = \infty$ and by Fatou's lemma $\int f_n \to \infty$. I am guessing that this is true somehow only with the Lebesgue measure, and not in other measure spaces? Othewise I don't understand how your example would be possible. | |
| Apr 1, 2018 at 20:15 | comment | added | coudy | @lcv this is an extension of the monotone convergence theorem. The function is assumed to be non-negative. | |
| Apr 1, 2018 at 19:41 | comment | added | lcv | Is this an extension of the monotone convergence or the dominated convergence theorem? | |
| Mar 30, 2018 at 13:48 | comment | added | Arnaud D. | According to this MSE question, this theorem appears in at least one textbook : math.stackexchange.com/questions/2713020/… | |
| S Mar 29, 2018 at 19:43 | history | answered | coudy | CC BY-SA 3.0 | |
| S Mar 29, 2018 at 19:43 | history | made wiki | Post Made Community Wiki by coudy |