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Dimension of slices through the Sierpinski carpet
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Manning, Anthony and Simon, Károly (2012) Dimension of slices through the Sierpinski carpet. Transactions of the American Mathematical Society, Volume 365 (Number 1). pp. 213-250. doi:10.1090/S0002-9947-2012-05586-3 ISSN 0002-9947.
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Official URL: http://dx.doi.org/10.1090/S0002-9947-2012-05586-3
Abstract
For Lebesgue typical , the intersection of the Sierpinski carpet with a line has (if non-empty) dimension , where . Fix the slope . Then we shall show on the one hand that this dimension is strictly less than for Lebesgue almost every . On the other hand, for almost every according to the angle -projection of the natural measure on , this dimension is at least . For any we find a connection between the box dimension of this intersection and the local dimension of at .
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 365 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 213-250 | ||||
DOI: | 10.1090/S0002-9947-2012-05586-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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