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

Chaoyi Zeng, Dehui Yuan & Shaoyuan Xu

DOI: 10.4208/ata.2012.v28.n1.4

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

Published online: 2012-03

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  • 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$.

  • Keywords

Sierpinski carpet, Hausdorff measure, upper convex density.

  • AMS Subject Headings

28A78, 28A80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-28-27, author = {}, title = {The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {1}, pages = {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$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2012.v28.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4538.html} }
TY - JOUR T1 - The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon JO - Analysis in Theory and Applications VL - 1 SP - 27 EP - 37 PY - 2012 DA - 2012/03 SN - 28 DO - http://doi.org/10.4208/ata.2012.v28.n1.4 UR - https://global-sci.org/intro/article_detail/ata/4538.html KW - Sierpinski carpet, Hausdorff measure, upper convex density. AB -

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$.

Chaoyi Zeng, Dehui Yuan & Shaoyuan Xu. (1970). The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon. Analysis in Theory and Applications. 28 (1). 27-37. doi:10.4208/ata.2012.v28.n1.4
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