Sierpinski地毯的Hausdorff测度的一个估计

Estimating the Hausdorff Measure of a Sierpinski Carpet

目的:对一种Sierpinski地毯进行Hausdorff测度的上限估计.方法:推广Hausdorff测度的次可数可加性,并利用Sierpinski地毯的对称性,改进文献[1]中的覆盖.结果文献[1]得到上限估计Hs(S)≤1.409 736 1,经改进后得到Hs(S)≤1.396 434 226 4.结论:Hausdorff测度的次可数可加性的推广以及对称性可以应用于研究其他一些分形集的情形.

Aim for a special type of sierpinski carpet,we try to obtain the estimate value of the upper limit of its hausdorff measure.Methods by generalizing the countable subadditivity of hausdorff measure and using the symmetry of the sierpinski carpet,the author improves a coving of sierpinski carpet in literature^[1].Results in literature^[1],the estimate value of the upper limit is1.4097361,we improves it and gets.Conclusion The generalization of the countable subadditivity of hausdorff measure and the symmetry can be used in some other fractal set.