一个Sierpinski垫片的Hausdorff测度的准确值的计算

The Calculation of the Exact Value for Hausdorff Measure of Sierpinski Carpet

研究了一个Sierpinski垫片的Hausdorff测度,利用自相似集Hausdorff测度的上限估计的有效方法,得到Sierpinski垫片的Hausdorff测度的一个上界,然后应用垂直射影的方法得到Hausdorff测度的一个下界,从而得到该Sierpinski垫片的Hausdorff测度的准确值.

A Hausdorff measure of Sierpinski car pet was studied in this paper. First, we got a upper bound of Hausdorff measure of Sierpinski carpet by an effective method of lower bound for the simple fractal of Hausdorff measure. Then we got the upper bound of Hausdorff measure of Sierpinski carpet by the method of the Vertical mapping principle. Thus the exect value of this Sierpinski carpet was presented. At the same time,this method was more simple than others.