Abstract
We prove that a purely unrectifiable self-similar set of finite 1-dimensional Hausdorff measure in the plane, satisfying the Open Set Condition, has radial projection of zero length from every point.
| Original language | English |
|---|---|
| Pages (from-to) | 67-78 |
| Number of pages | 12 |
| Journal | Real Analysis Exchange |
| Volume | 32 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2007 |
| Externally published | Yes |
Bibliographical note
Funding Information:Key Words: Hausdorff measure, purely unrectifiable, self-similar set Mathematical Reviews subject classification: Primary 28A80 Received by the editors October 23, 2005 Communicated by: Clifford E. Weil ∗Supported in part by OTKA Foundation grant T42496. †supported in part by NSF grant DMS-0355187. ‡This collaboration was supported by NSF-MTA-OTKA grant #77.
Funding
Key Words: Hausdorff measure, purely unrectifiable, self-similar set Mathematical Reviews subject classification: Primary 28A80 Received by the editors October 23, 2005 Communicated by: Clifford E. Weil ∗Supported in part by OTKA Foundation grant T42496. †supported in part by NSF grant DMS-0355187. ‡This collaboration was supported by NSF-MTA-OTKA grant #77.
| Funders | Funder number |
|---|---|
| NSF-MTA-OTKA | 77. |
| OTKA Foundation | T42496 |
| Directorate for Mathematical and Physical Sciences | 0355187 |
| National Science Foundation | DMS-0355187 |
Keywords
- Hausdorff measure
- Purely unrectifiable
- Self-similar set