The Hausdorff dimension of sets related to the general Sierpinski carpets

被引：1
|
作者：
Gui, Yong Xin [1 ,2 ]
Li, Wen Xia [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
[2] Xianning Coll, Dept Math, Xianning 437005, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2010年 / 26卷 / 04期
基金：
中国国家自然科学基金;
关键词：
general Sierpinski carpets; Hausdorff dimension; Hausdorff measure;
D O I：
10.1007/s10114-010-7453-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study a class of subsets of the general Sierpinski carpets for which the allowed two digits in the expansions occur 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 finite.
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页码：731 / 742
页数：12
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