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

作　　者：Yong Xin GUI 

机构地区：[1]Department of Mathematics, Xianning College, Xianning 437100, P. R. China [2]Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第7期1369-1382,共14页数学学报（英文版）

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

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.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.

关 键 词：the general Sierpinski carpets Hausdorff dimension Hausdorff measure 

分 类 号：O174.12[理学—数学] TQ546[理学—基础数学]