一类Sierpinski地毯的packing测度

The packing measure of sierpinski carpets

设E为R2 上的压缩比为1m(m≥4)的Sierpinski地毯.利用E的自相似性计算集E的关于其Hausdor ff测度的下密度值,进而得到了E的packing测度的准确值。

Let E in R2 be a sierpinski carpet with a contracting similar ratio 1m(m≥4).In this paper,we calculate the lower density of s-dimensional Hausdorff measure on E by the self-similarity of E.Furthermore,the exact value of the packing measure for E is obtained.