Hausdorff Dimension and Measure of a Class of Subsets of the General Sierpinski Carpets

作     者：Yong Xin GUI 

作者机构：Department of Mathematics Xianning College Xianning 437100 P. R. China Department of Mathematics East China Normal University Shanghai 200062 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2010年第26卷第7期

页      面：1369-1382页

核心收录：

学科分类：081702[工学-化学工艺] 07[理学] 08[工学] 0817[工学-化学工程与技术] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Educational Office of Hubei Province #Q20082802 the Science and Technology Commission of Shanghai Municipality #06ZR14029 

主　　题：the general Sierpinski carpets Hausdorff dimension Hausdorff measure 

摘      要：In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions with proportional frequency. We calculate the Hausdorff and Box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.