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The packing measure of self-affine carpets

Published online by Cambridge University Press:  24 October 2008

Yuval Peres
Yuval Peres
Affiliation:
Yale University, Department of Mathematics, New Haven, CT 06520
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Abstract

We show that the seif-affine sets considered by McMullen [15] and Bedford [2] have infinite packing measure in their packing dimension θ except when all non-empty rows of the initial pattern have the same number of rectangles. More precisely, the packing measure is infinite in the gauge tθ|logt|−1 and zero in the gauge tθ|logt|−1−δ for any δ > 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 3 , May 1994 , pp. 437 - 450
Copyright
Copyright © Cambridge Philosophical Society 1994

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