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《Journal of Jiangxi Normal University (Natural Sciences Edition)》 2004-03
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A Necessary and Sufficient Condition for a Self-Similar Set to Have Best-a.e. Cover Consisting of Closed Sets

XU Shao-yuan~(1,2),LI Guo-zhen~3 (1.Dept. of Math. Huaibei Coal Industry Teachers' College, Huaibei 235000,China;2.College of Mathematics and Scientific Computer, Zhongshan University, Guangzhou 510275,China;3.Institute of Mathematics and Informatics,Jiangxi Normal University, Nanchang 330027,China)  
Using the partly estimating principle for the self-similar sets and the vitali covering theorem, we obtain a necessary and sufficient condition for a self-similar set to have best -a.e. cover consisting of closed sets.
【Key Words】: self-similar set Hausdorff measure and dimension best -a.e.covering
【Fund】: 国家自然科学基金资助项目(10171116);; 广东省自然科学基金资助项目(011221);; 安徽省教育厅重点科研资助项目(2003kj047zd).
【CateGory Index】: O174.12
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1 XU Shao-yuan(School of Mathematics and Computer Science,Gannan Teachers College,Ganzhou Jiagxi 341000,China);A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best-a.e.-Closed-Set Covering[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2007-03
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【Citations】
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1 Xu Shaoyuan (Huaibei Coal Industry Teachers' College, Huaibei, Anhui, 235000, P. R. China);On a Criterion of the Hausdorff Measure of the Self-similar Sets and Applications[J];Advances In Mathematics;2002-02
2 WEN Sheng You (Department of Mathematics, Hanshan Teacher's College, Chaozhou 521041, P. R. China) (Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China) XU Shao Yuan (Department of Mathematics, Huaibei Coal Industry Teacher's College,;On Hausdorff Measures of Self-Similar Sets[J];Acta Mathematica Sinica;2001-01
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【Co-citations】
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1 SONG Shou bai,\ XIE Ming qin (Department of Mathematics, Anhui Normal University, 241000, Wuhu, Anhui, China);THE HAUSDORFF MEASURE OF KOCH CURVE[J];JOURNAL OF ANHUI NORMAL UNIVERSITY(NATURAL SCIENCE);1999-03
2 Shaoyuan Xu (Gannan Teachers College,China) Weiyi Su (Nanjing University,China);ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION[J];分析,理论与应用(英文版);2007-04
3 Shaoyuan Xu? (Huaibei Coal Industry Teachers College, China) Weiyi Su (Nanjing University, China) and Zuoling Zhou (Zhongshan University, China ) Received Jun.5, 2007; Revised Jan. 24, 2008;ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION[J];分析,理论与应用(英文版);2008-01
4 XU Shao-yuan(School of Mathematics and Computer Science,Gannan Teachers College,Ganzhou Jiagxi 341000,China);A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best-a.e.-Closed-Set Covering[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2007-03
5 ZENG Chao-yi(College of Mathematics and in formation technical,Hanshan Teachers College,Chaozhou 521041,China);Hausdorff measure of m non-uniform Cantor set[J];Pure and Applied Mathematics;2006-01
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7 YAN Kun(Xi'an Modern Nonlinear Science Applying Institute, Xi'an 710061, China);Fractal dimension structure of Cosmos and its mathematical foundations[J];Progress In Geophysics;2004-03
8 XUShao-yuan,CHENLiang(DepartmentofMathematics,HuaibeiCoalIndustryTeachersCollege,235000,Huaibei,Anhui,China);Some Notes on Developing Students′Ability to Make Scientific Research in Teaching of Real Variable Function[J];Journal of Huaibei Industry Teachers College (Natural Sciences Edition);2003-02
9 LIU Juan,XU Shao-yuan(Department of Mathematics,Huaibei Coal Industry Teachers College,235000,Huaibei,Anhui,China);The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself[J];Journal of Huaibei Coal Industry Teachers College(Natural Science Edition);2006-01
10 XU Shao-yuan,LIU Jing,CHEN Xiao-yun(Department of Mathematics,Huaibei Coal Industry Teachers College,235000,Huaibei,Anhui,China);The Hausdorff Dimension of the General Sierpinski Block Generated by Normal Tetrahedron and the Estimation of Its Hausdorff Measure[J];Journal of Huaibei Coal Industry Teachers College(Natural Science Edition);2007-04
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1 XU Shao yuan (Department of Mathematics,Huaibei Coal Industry Tearchers College,Huaibei 235000,China);A New Fixed Point Theorem for Increasing Operators and Its Applications[J];JOURNAL OF JIANGXI NORMAL UNIVERSITY (NATURAL SCIENCES EDITION);2000-01
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4 ZENG Chao-yi~1,XU Shao-yuan~2(1.Department of Mathematics,Hanshan Teachers College,Chaozhou 521041,China)(2.Department of Mathematics,Huaibei Coal Industry,Huaibei 235000,China);An Elementary Proof on the Hausdorff Measure of a Sierpinski Carpet[J];Mathematics in Practice and Theory;2006-02
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