Timeline for An uncountable measurable subset of $\Bbb R$ containing no nonempty perfect set
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 23 hours ago | vote | accept | Iosif Pinelis | ||
| yesterday | answer | added | bof | timeline score: 2 | |
| yesterday | answer | added | Jason Zesheng Chen | timeline score: 5 | |
| 2 days ago | comment | added | Dave L Renfro | Relevant is Classical theory of totally imperfect spaces by Jack Bethel Brown and Gregory Van Cox [Real Analysis Exchange 7 #2 (1981−1982), pp. 185−232]. | |
| 2 days ago | comment | added | Iosif Pinelis | @RonniePavlov : Thank you for your comment. | |
| 2 days ago | comment | added | Iosif Pinelis | @bof : Thank you for your comments. Can you collect them into a formal answer? Concerning your latter comment, I would feel more comfortable if you used Zorn's lemma instead of transfinite induction. | |
| 2 days ago | answer | added | Arno | timeline score: 6 | |
| 2 days ago | comment | added | Ronnie Pavlov | Isn't the property of being a Bernstein set invariant under complement, so the intersection of Cantor with one of Berstein or its complement must be uncountable? | |
| 2 days ago | comment | added | Iosif Pinelis | @bof : Will this intersection be uncountable? | |
| 2 days ago | comment | added | bof | Consider the intersection of the Cantor set with a Bernstein set. | |
| 2 days ago | comment | added | Iosif Pinelis | @AlekseiKulikov : I have added to my post the "On the other hand" response to your comment. | |
| 2 days ago | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 260 characters in body
|
| 2 days ago | history | edited | LSpice | CC BY-SA 4.0 |
Removing initial whitespace
|
| 2 days ago | comment | added | Aleksei Kulikov | Are you sure you want Lebesgue-measurable and not Borel-measurable? I think if you start with some set of measure zero (say, the Cantor set), all of its subsets are Lebesgue-measurable, and then I think you can find by the same procedure with the axiom of choice the required subset of it. | |
| 2 days ago | history | asked | Iosif Pinelis | CC BY-SA 4.0 |