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The Hausdorff and Packing Dimensions of Some Sets Related to Sierpiński Carpets

Published online by Cambridge University Press:  20 November 2018

Ole A. Nielsen
Ole A. Nielsen*
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario email: nielseno@post.queensu.ca
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Abstract

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The Sierpiński carpets first considered by C.McMullen and later studied by Y. Peres are modified by insisting that the allowed digits in the expansions occur with prescribed frequencies. This paper (i) calculates the Hausdorff, box (or Minkowski), and packing dimensions of the modified Sierpiński carpets and (ii) shows that for these sets the Hausdorff and packing measures in their dimension are never zero and gives necessary and sufficient conditions for these measures to be infinite.

Keywords

28A7828A80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 5 , 01 October 1999 , pp. 1073 - 1088
Copyright
Copyright © Canadian Mathematical Society 1999

References

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