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2007/2008 The Centered Covering Measures of a Class of Self-Similar Sets on the Plane
Zuoling Zhou, Zhiwei Zhu
Real Anal. Exchange 33(1): 217-234 (2007/2008).

Abstract

Let $S \subset R^2$ be the attractor of the iterated function system $\{f_1,f_2,f_3, f_4\}$, where $f_i(x)=\lambda_i x+b_i$, $i=1,2,3,4$, $x=(x_1,x_2) \in R^2$, $0<\lambda_i \le \frac{1}{2+\sqrt{2}}$,$b_1=(0,0)$, $b_2=(1-\lambda_2, 0)$, $b_3=(1-\lambda_3,1-\lambda_3)$, and $b_4=(0, 1-\lambda_4)$. This paper determines the exact centered covering measure of $S$ under some conditions relating to the contraction parameters.

Citation

Download Citation

Zuoling Zhou. Zhiwei Zhu. "The Centered Covering Measures of a Class of Self-Similar Sets on the Plane." Real Anal. Exchange 33 (1) 217 - 234, 2007/2008.

Information

Published: 2007/2008
First available in Project Euclid: 28 April 2008

zbMATH: 1151.28006
MathSciNet: MR2402874

Subjects:
Primary: 28A78 , 28A80

Keywords: Centered covering measure , densit , self-similar sets

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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