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 - <p style="text-align: justify;">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$.</p>