The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon

The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon

Year:    2012

Analysis in Theory and Applications, Vol. 28 (2012), Iss. 1 : pp. 27–37

Abstract

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

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2012.v28.n1.4

Analysis in Theory and Applications, Vol. 28 (2012), Iss. 1 : pp. 27–37

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

Keywords:    Sierpinski carpet Hausdorff measure upper convex density.

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