Timeline for Measure between the counting measure and the Lebegue measure
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2010 at 12:04 | vote | accept | Sune Jakobsen | ||
| Jan 13, 2010 at 10:26 | comment | added | Thorny | If a set has positive, finite d-dimensional measure (and it is easy to create for example a self-similar Cantor set with a prescribed Hausdorff dimension), then it has measure 0 according to any d'-dimensional Hausdorff measure with d'>d and has infinite measure according to any d"-dimensional Hausdorff measure with d"<d. | |
| Jan 13, 2010 at 9:41 | comment | added | Matus Telgarsky | the conditions require that there exists a set with lebesgue measure 0 but infinite measure according to this measure. Are you sure this holds for Hausdorff measure (with dimension in $(0,1)$)? | |
| Jan 13, 2010 at 9:27 | comment | added | Pete L. Clark | Acknowledgment: My response is independent of Thorny's but came slightly later. | |
| Jan 13, 2010 at 9:24 | comment | added | Thorny | And I guess adding Hausdorff measures with gauge functions would give even more examples, which aren't all that easy to works with though. | |
| Jan 13, 2010 at 9:22 | history | answered | Thorny | CC BY-SA 2.5 |