Timeline for Example of function of bounded variation but not absolutely continuous. [closed]
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2012 at 8:47 | vote | accept | KNS | ||
| Jun 22, 2012 at 15:48 | history | closed |
George Lowther Bill Johnson Emil Jeřábek Willie Wong S. Carnahan♦ |
off topic | |
| Jun 22, 2012 at 15:35 | answer | added | Thomas | timeline score: 1 | |
| Jun 22, 2012 at 14:08 | comment | added | Ricky | When you are looking for a counterexample in analysis you should always have a look at the very beautiful "counterexamples in analysis" by Gelbaum and Olmsted (books.google.de/…). It is very likely it contains what you are looking for. | |
| Jun 22, 2012 at 14:05 | comment | added | Pietro Majer | Other examples: $f(x)=\mu([0,x))$, where $\mu$ is a measure supported in a Lebesgue null set. The Cantor function is of this form, and in fact every BV function, up to removing an absolutely continuous part. | |
| Jun 22, 2012 at 13:24 | comment | added | Gerald Edgar | And if you don't require continuity, just take a simple jump: $f(x)=0$ for $x<0$ and $f(x)=1$ for $x \ge 1$. | |
| Jun 22, 2012 at 13:13 | comment | added | Michael Greinecker | math.stackexchange.com/questions/4683/… | |
| Jun 22, 2012 at 12:59 | history | asked | KNS | CC BY-SA 3.0 |