一个经典分形集的Hausdorff测度的上界估计

摘要

研究经典分形集Sierpinski三角垫的Hausdo廿测度的上界估计，构造了Sierpinski5-垫的某种覆盖六边形，给出了这个覆盖集中小三角形的个数以及覆盖的直径的计算公式，据此获得了Sierpinski三角垫的Hausdorff测度的一个更好的上界估计值Hs（S）≤137781/109286×（2431/3072）s≈0.870 031 853.%Abstract： The central task on the investigation of the fractal sets is to calculate or estimate Haus- dorff dimension and Hausdorff measure. In this paper, the upper bound estimation on Hausdorff mea- sure of Sierpinski gasket is investigated. The laws about the number of small triangles which are sum- marized in the coverage and the diameter of the coverage are summed up by the part-estimation method.Using these laws, a better upper bound estimation value Hs（S）≤137781/109286×（2431/3072）s≈0.870 031 853 on the Sierpinski gasket is obtained.