一类广义Cantor集Hausdorff测度的计算  

On calculation of the Hausdorff measure of a kind of generalized Cantor set

作　　者：胡晓梅[1] 

机构地区：[1]咸宁学院数学与统计学院,湖北咸宁437100

出　　处：《黄冈师范学院学报》2010年第6期40-42,共3页Journal of Huanggang Normal University

基　　金：咸宁学院科研资助项目(ky09060)

摘　　要：将三分Cantor集构造的一个性质推广到2n+1(n∈N)分Cantor集,并用它简便计算出2n+1分Cantor集的Hausdorff测度,给出了此类广义Cantor集Hausdorff测度计算的一种新方法.该方法比其它方法更为初等而易于计算,为计算其它分形集的Hausdorff测度提供了一种思路.By means of generalizing one property of Cantor ternary set to Cantor-2n＋1（n∈N） fractal set and applying it to calculate the Hausdorff measure of Cantor-2n＋ 1（n∈N） fractal set,this paper presents a new method of calculating Hausdorff measure of generalized Cantor set.Compared with other methods,this method can be more conveniently calculated with elementary knowledge,and can provide some reference for the calculation of Hausdorff measure of other Cantor sets.

关 键 词：2n+1分Cantor集 HAUSDORFF测度 k-级基本区间 

分 类 号：O174.12[理学—数学]