The Hausdorff Measure of Sierpinski Carpets Basing on Regular Pentagon
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@Article{ATA-28-27,
author = {Chaoyi Zeng, Dehui Yuan and Shaoyuan Xu},
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
AU - Chaoyi Zeng, Dehui Yuan & Shaoyuan Xu
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 and Shaoyuan Xu. (2012). 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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