Volume 28, Issue 1
The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon

Chaoyi Zeng ,  Dehui Yuan and Shaoyuan Xu

10.4208/ata.2012.v28.n1.4

Anal. Theory Appl., 28 (2012), pp. 27-37

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  • Abstract

In this paper, we address the problem of exact computation of the Hausdorffmeasure of a class of Sierpinski carpets E− the self-similar sets generating in a unit regularpentagon on the plane. Under some conditions, we show the natural covering is the bestone, and the Hausdorff measures of those sets are euqal to $|E|^s$, where $ s = dim_{H}E$.

  • History

Published online: 2012-03

  • AMS Subject Headings

28A78, 28A80

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