一个笛卡尔乘积的Hausdorff维数

The Hausdorff Dimension of Descartes Product Set

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.