摘要
设S_λ为压缩比为λ(λ≤1/3)的一类Sierpinski垫,s=-log_λ3为S_λ的Hausdorff维数,N为产生S_λ的所有基本三角形的集合.本文使用网测度方法,获得了S_λ的s-维Hausdorff测度的精确值H^s(S_λ)=1,同时证明了H^s(S_λ)可由S_λ关于网N的s-维Hausdorff测度H_N^s(S_λ)确定,获得了S_λ的非平凡的最佳覆盖.
Let Sλ be a class of Sierpinski gaskets with compression ratio λ （λ ≤ 1/3）, s = - logλ^3 be the Hausdorff dimension of Sλ, and N be the set of all the basic triangles to produce Sλ. In the paper, by the method of net measure, the exact value of the Hausdorff measure of Sλ, H^s（Sλ） = 1, is obtained, the fact that the Hausdorff measure of Sλ can be determined by net measure HN^s（Sλ） is shown, and the best coverings of Sλ that are nontrivial are obtained.
基金
重庆市教育委员会科学技术研究项目(KJ051206)
