Timeline for Construction of nonmeasurable sets
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2014 at 2:01 | comment | added | Bob Solovay | Re Asaf's remark. Yes, I had this result first. Something very like my proof of this was subsequently published by Sacks. | |
| Sep 4, 2014 at 1:57 | comment | added | Bob Solovay | As I recall, Cohen didn't mention "countable choice". But this was an off hand remark (posing the problem) at the end of his lecture. It seemed to me at the time I did this stuff that full DC was needed for the Radon-Nikodym theorem. But as I recall, I convinced myself a few years ago that a different proof of Radon-Nikodym than the one given in Halmos could be done with just AC_omega. | |
| Aug 29, 2014 at 14:59 | comment | added | Andreas Blass | Did Cohen not even mention countable choice of reals in this connection? That seems needed just to get Lebesgue measure theory started (e.g., proving countable additivity). As far as I can see, DC becomes important only in "higher" parts of the theory. (To formulate a specific conjecture: Countable choice suffices for all the measure theory that we require graduate students to know for their qualifying exams.) | |
| Aug 29, 2014 at 1:26 | comment | added | Asaf Karagila♦ | If my memory serves me right, first came the proof that the Lebesgue measure can be extended to all sets (without choice, and without large cardinals, of course), right? | |
| Aug 29, 2014 at 1:18 | vote | accept | Monroe Eskew | ||
| Aug 29, 2014 at 0:48 | history | answered | Bob Solovay | CC BY-SA 3.0 |