Sierpinski垫片的Hausdorff测度的上界估计

Upper Bound Estimation on Hausdorff Measure of Sierpinski Gasket

研究分形集的中心任务是计算或估计分形集的Hausdorff维数与Hausdorff测度。本文研究Sierpinski垫片的Hausdorff测度的上界估计,利用部分估计的方法,归纳出了关于Sierpinski垫片的某种部分覆盖所包含的小三角形的个数以及这种覆盖的直径的规律,得到了Sierpinski垫片的Hausdorff测度的一个更好的上界估计值Hs(S)≤1377811/09286×(2431/3072)s≈0.870031853。

The central task on the investigation of the fractal sets is to calculate or estimate Hausdorff dimension and Hausdorff measure. In this paper, the upper bound estimation on Hausdorff measure of Sierpinski gasket is investigated. The laws about the number of small triangles which are summarized 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 H^s（S） ≤1377811/09286×（2431/3072）^s≈0.870031853 on the Sierpinski gasket is obtained.