Timeline for When will the upper regularization of a bounded function not defined?
Current License: CC BY-SA 3.0
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Apr 21, 2017 at 4:49 | history | bounty ended | CommunityBot | ||
| S Apr 21, 2017 at 4:49 | history | notice removed | CommunityBot | ||
| Apr 16, 2017 at 13:39 | history | edited | Idonknow | CC BY-SA 3.0 |
added 175 characters in body
|
| Apr 16, 2017 at 0:22 | comment | added | Idonknow | Reply from Professor Kechris: It has been a very long time since I have thought about this subject but taking a quick look again in the paper, it appears that indeed the case ξ=1 is missing. Thanks for pointing this out. | |
| Apr 14, 2017 at 17:36 | comment | added | Todd Leason | If they reply, please let us know what they say. | |
| Apr 14, 2017 at 14:43 | comment | added | Idonknow | @ToddLeason: Okay, I will try to email authors. | |
| Apr 14, 2017 at 5:12 | comment | added | Todd Leason | ... But the induction hypothesis hasn't been proved for $\xi_n = 1$, since the induction starts with $\xi=0$. So, in my opinion, the induction is missing the case $\xi=1$. If I where you, I would write to the authors and ask about this issue. However, I don't know if they're still active. | |
| Apr 14, 2017 at 5:11 | comment | added | Todd Leason | Taking $\xi = 1$ in the paper's Theorem 4 (ii) (in section 3) should give an example. However, the proof is based on Lemma 3 and I don't see how the inductive proof of Lemma 3 works for countable ordinals: It starts with $\xi = 0$. Thus, the case $\xi = 1 = 0 + 1$ should follow from Case 3 for $\xi = 0$. But Case 3 requires an strictly increasing sequence $\xi_n$ with $\sup \xi_n = \omega^\xi=\omega^0=1$ (hence the sequence ends with $\xi_n = 1$) such that the induction hypothesis holds for all $\xi_n$. ... | |
| Apr 13, 2017 at 15:02 | history | edited | Idonknow | CC BY-SA 3.0 |
added 58 characters in body
|
| Apr 13, 2017 at 14:40 | comment | added | Idonknow | @ToddLeason: I am interested to see an example of a function $f$ such that $f_{\xi}$ is not defined for some $\xi$. | |
| Apr 13, 2017 at 14:38 | history | edited | Idonknow | CC BY-SA 3.0 |
added 3 characters in body
|
| Apr 13, 2017 at 14:26 | comment | added | Todd Leason | "Question: When will the function $f_{\xi}$ not [be] defined ?" -- What kind of answer do you expect ? Do you want a classification of functions $f$ such that that $f_{\xi}$ isn't defined for some ordinal $\xi$ or do you want to see an explicit example of such a function $f$ ? | |
| Apr 13, 2017 at 12:20 | history | edited | Idonknow | CC BY-SA 3.0 |
added 565 characters in body
|
| Apr 13, 2017 at 11:26 | comment | added | Idonknow | They do not give any example. They define the upper regularization for bounded function but yet, they say the upper regularization might not be defined. | |
| Apr 13, 2017 at 7:17 | comment | added | Tommi | You write, in the question, that the authors write that $\hat f$ might not be defined. Do they give examples or do they mean that it might not be defined for unbounded functions? | |
| Apr 13, 2017 at 7:10 | comment | added | Idonknow | For bounded function $f $, I do not know any. | |
| Apr 13, 2017 at 6:56 | comment | added | Tommi | Do you know examples where $\hat f$ is not defined? | |
| S Apr 13, 2017 at 3:41 | history | bounty started | Idonknow | ||
| S Apr 13, 2017 at 3:41 | history | notice added | Idonknow | Draw attention | |
| Apr 13, 2017 at 3:40 | history | edited | Idonknow | CC BY-SA 3.0 |
deleted 99 characters in body
|
| Apr 9, 2017 at 10:54 | history | asked | Idonknow | CC BY-SA 3.0 |