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O'Neil, Toby
(2007).
URL: http://www.ams.org/tran/2007-359-11/S0002-9947-07-...
Abstract
For a compact set and a point
, we define the visible part of
from
to be the set
(Here denotes the closed line segment joining
to
.)
In this paper, we use energies to show that if is a compact connected set of Hausdorff dimension larger than one, then for (Lebesgue) almost every point
, the Hausdorff dimension of
is strictly
less than the Hausdorff dimension of . In fact, for almost every
,
We also give an estimate of the Hausdorff dimension of those points
where the visible set has dimension larger than for
.
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About
- Item ORO ID
- 2141
- Item Type
- Journal Item
- ISSN
- 0002-9947
- Keywords
- Hausdorff dimension; connected; visible sets
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Depositing User
- Toby O'Neil