一类Sierpinski地毯的Hausdorff测度的初等证明

An elementary proof for the Hausdorff measure of some Sierpinski carpets

在平面上以直径为d(d>0)的正M边形为基本集(M≥3为整数),构造压缩比为1∶k(k为不小于M的实数)的广义Sierpinski地毯,并用初等方法计算出它的Hausdorff测度为ds,其中s=logkM.

Based on the Mrightpolygon with the diameter d>0 and an integer M≥3, a kind of generalized Sierpinski carpets with a contract radio 1∶k(k≥M is a real number) is constructed, and its Hausdorff measure is proved to be ds, where s=logkM.