Timeline for Lebesgue measure of the graph of a function [closed]
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2011 at 15:54 | history | closed |
Gerry Myerson Mark Meckes George Lowther Andrés E. Caicedo Anton Petrunin |
too localized | |
| Apr 28, 2011 at 13:01 | comment | added | Joel David Hamkins | I posted an answer over at math.stackexchange.com/questions/35606/…. One can build a function using the axiom of choice, whose graph is not contained in any $G_\delta$ set with less than full measure. Thus, the graph has full outer measure. Meanwhile, the inner measure must always be zero, since there are uncountably many disjoint vertical translations. | |
| Apr 28, 2011 at 12:10 | comment | added | Gerry Myerson | Since it has now been posted to m.se (it's question 35606 there), I guess we can close it here. | |
| Apr 28, 2011 at 12:06 | answer | added | Stefan Geschke | timeline score: 5 | |
| Apr 28, 2011 at 11:55 | comment | added | Cosmonut | OK, I will post it there instead | |
| Apr 28, 2011 at 11:36 | comment | added | Mark | Note that if $f$ is non-measurable then the graph of $f$ is not a measurable set, so in this case you should probably ask if it has positive inner measure (or outer measure). | |
| Apr 28, 2011 at 11:33 | comment | added | camomille | More appropriate for math.stackexchange.com | |
| Apr 28, 2011 at 11:09 | history | asked | Cosmonut | CC BY-SA 3.0 |