IJPAM: Volume 61, No. 3 (2010)

THE HAUSDORFF MEASURE OF A CLASS OF
SIERPINSKI CARPETS ON THE PLANE

Chaoyi Zeng$^1$, Dehui Yuan$^2$
$^{1,2}$Department of Mathematics
Hanshan Normal University
Chaozhou, Guangdong, 521041, P.R. CHINA
$^1$e-mail: zcy@hstc.edu.cn
$^2$e-mail: ydhlxl@hstc.edu.cn


Abstract.In this paper, we address the problem of exact computation of the Hausdorff measure of a class of Sierpinski carpets -- the self-similar sets generating in unit regular pentagon on plane. Under some conditions, we get the natural covering is the best one, and the Hausdorff dimension of those sets are euqal to $\vert E\vert^s$, where $s=\text{\rm dim}_HE$.

Received: March 18, 2010

AMS Subject Classification: 28A78, 28A80

Key Words and Phrases: Sierpinski carpet, Hausdorff measure, upper convex density

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 3