对称Cantor集自乘积集的Hausdorff中心测度

The Hausdorff Centered Measure of the Cartesian Product of the Symmetric Cantor Set with Itself

设Cλ是由迭代函数系统(IFS){f1,f2}生成的对称Cantor集,其中f1(x)=λx, f2(x)=1-λ+λx,0<λ<1/2,x∈[0,1]．在压缩比λ满足一定条件时,本文得到了Cλ与其自身的笛卡尔乘积Cλ×Cλ的Hausdorff中心测度的计算公式．

Let Cλ be the symmetric Cantor set generated by the iterated function system （IFS）{fl, f2}, where f1（x） = λx, f2（x） = 1 - λ ＋ λx, 0 〈 λ 〈 1/2, x ∈ [0, 1]. In this paper, we determine the exact Hausdorff centered measure of Cλ × Cλ under some conditions.