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

作　　者：ZENG Chao-yi 

机构地区：[1]College of Mathematics and Information Technology, Hanshan Teacher＇s College, Chaozhou 521041,China

出　　处：《Chinese Quarterly Journal of Mathematics》2006年第2期293-296,共4页数学季刊（英文版）

基　　金：Supported by the Scientific Research of Hanshan Teacher's College(2004)

摘　　要：The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration （1）： Si（x） = αix ＋ bi, x ∈ [0, 1], i = 1,2,…, m, where 0 〈 αi 〈 1, i = 1,2,…,m; bi ＋ αi 〉 0, i = 1,2,…,m- 1, b1 = 0 and αm ＋ bm = 1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

关 键 词：self-similar set Cantor set Hausdorff dimension Hausdorff measure 

分 类 号：O174.12[理学—数学]