(4m+1)分Cantor集Hausdorff维数与测度的近似估计

Estimation of Hausdorff Measure and Dimension of the Cantor⁃4 m+1 Fractal Sets

本文对三分Cantor集进行适当的推广,构造出一类(4m+1)(m∈N)分Cantor集,并计算其Hausdorff维数与测度;依据三分Cantor集和引理给出(4m+1)(m∈N)分Cantor集Hausdorff维数与测度的几种新颖的方法;以定理的形式给出(4m+1)分Cantor集其Hausdorff维数s=log_(4m+1)(2m+1)和s⁃维Hausdorff测度H_(s)(F_(1))=1.

In this paper,we construct a class of cantor⁃4m+1 fractal sets which is the promotion of Cantor set,and then calculate its Hausdorff measure and dimension.Based on previous conclusions of Cantor set and lemmas,several novel methods are given to calculate the Hausdorff measure and dimension of cantor⁃4 m+1 fractal sets(m∈N).The results are given in the form of theorems which the Hausdorff measure and dimension of cantor⁃4m+1 fractal sets respectively are s=log_(4m+1)(2m+1)and H_(s)(F_(1))=1.