O'Neil, Toby
(2007).

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URL:  http://www.ams.org/tran/200735911/S0002994707... 

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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 .
Item Type:  Journal Article 

ISSN:  00029947 
Keywords:  Hausdorff dimension; connected; visible sets 
Academic Unit/Department:  Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology 
Item ID:  2141 
Depositing User:  Toby O'Neil 
Date Deposited:  15 Aug 2007 
Last Modified:  15 Jan 2016 19:48 
URI:  http://oro.open.ac.uk/id/eprint/2141 
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