Hausdorff centered measure of certain linear Cantor sets  

作　　者：PENGLi WUMin 

机构地区：[1]DepartmentofMathematics,HubeiUniversity,Wuhan430062,China [2]DepartmentofAppliedMathematics,SouthChinaUniversityofTechnology,Guangzhou510640,China

出　　处：《Progress in Natural Science:Materials International》2005年第4期297-303,共7页自然科学进展·国际材料（英文版）

基　　金：SupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .10 1710 2 8)andMorningsideCenterofMathematics

摘　　要：In this paper, we study the Hausdorff centered measure of certain linear Cantor sets. We establish the relationship between the Hausdorff centered measure of this set and the maximum centered density of the corresponding self similar measure. From this relationship, the Hausdorff centered measure of certain sets is obtained. In particular, we consider the linear iterated function system consisting of three maps with the same contraction ratios. Under some technical restrictions, we determine the exact Hausdorff centered measure of its attractor.In this paper, we study the Hausdorff centered measure of certain linearCantor sets. We establish the relationship between the Hausdorff centered measure of this set andthe maximum centered density of the corresponding self-similar measure. From this relationship, theHausdorff centered measure of certain sets is obtained. In particular, we consider the lineariterated function system consisting of three maps with the same contraction ratios. Under sometechnical restrictions, we determine the exact Hausdorff centered measure of its attractor.

关 键 词：Hausdorff centered measure packing measure Cantor set 

分 类 号：TB9[一般工业技术—计量学]