广义长方形Sierpinski地毯的Hausdorff测度

The Hausdorff Measure of Sierpinski Carpet on Rectangle

利用Sierpinski地毯的自相似结构。得到Hausdorff测度的上界，通过在Sierpinski地毯上定义一个质量分布，利用质量分布原理得到测度的下界，从而得到了所定义的长方形Sierpinski地毯的Hausdorff测度的准确值。

This paper takes use of self-similarity construction of Sierpinski carpet, the supper boundary of the Hausdorff measure is obtained. By defining mass distribution on Sierpinski carpet, the inferior boundary is given according to the principle of mass distribution. Therefore the exact value of the Hausdorff measure is determined.