一个笛卡尔乘积的Hausdorff维数  

The Hausdorff Dimension of Descartes Product Set

作　　者：柳艳[1] 

机构地区：[1]南京工程学院基础部,江苏南京211167

出　　处：《南京工程学院学报（自然科学版）》2010年第3期1-4,共4页Journal of Nanjing Institute of Technology(Natural Science Edition)

摘　　要：介绍了康托型集的几个性质,讨论一类笛卡尔乘积,在dimHE<1存在一个集合F,其维数满足dimH(E×F)=dimHE+dimHF的情况.进而构造一类Borel集,使得dimH(E×F)=dimHE+dimHF成立.This paper introduces some features of Cantor set and discusses Descartes product set.If dimHE1,there is a set of F,the dimension of which observes the condition in which dimH（E×F）=dimHE＋dimHF.Then Borel set that makes dimH（E×F）=dimHE＋dimHF is established.

关 键 词：笛卡尔乘积 HAUSDORFF维数 康托型集 BOREL集 

分 类 号：O189.12[理学—数学]