广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明

数学季刊 ›› 2006, Vol. 21 ›› Issue (2): 293-296.

广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明

College of Mathematics and Information Technology, Hanshan Teacher's College, Chaozhou 521041, China

收稿日期:2004-12-25 出版日期:2006-06-30 发布日期:2023-12-12
作者简介:ZENG Chao-yi(1958-),male,native of Shaodong,Hunan,an associate professor of Hanshan Teacher's College,engages in fractal geometry.
基金资助:
Supported by the Scientific Research of Hanshan Teacher’s College(2004)；

The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist

College of Mathematics and Information Technology, Hanshan Teacher's College, Chaozhou 521041, China

Received:2004-12-25 Online:2006-06-30 Published:2023-12-12
About author:ZENG Chao-yi(1958-),male,native of Shaodong,Hunan,an associate professor of Hanshan Teacher's College,engages in fractal geometry.
Supported by:
Supported by the Scientific Research of Hanshan Teacher’s College(2004)；

摘要/Abstract

摘要： The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1):S_i(x)=a_ix+b_i,x∈[0,1], i=1, 2,…,m, where 0<a_i< 1, i=1, 2,…, m; b_i+a_i>0, i=1, 2,…, m-1, b1=0 and a_m+b_m=1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

关键词: , self-similar set, Cantor set, Hausdorff dimension, Hausdorff measure

Abstract: The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1):S_i(x)=a_ix+b_i,x∈[0,1], i=1, 2,…,m, where 0<a_i< 1, i=1, 2,…, m; b_i+a_i>0, i=1, 2,…, m-1, b1=0 and a_m+b_m=1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

Key words: , self-similar set, Cantor set, Hausdorff dimension, Hausdorff measure

中图分类号:

O174.12

曾超益. 广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明[J]. 数学季刊, 2006, 21(2): 293-296.

ZENG Chao-yi . The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 293-296.

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