摘要
设Sm为压缩比为1/m（m≥4）的Sierpinski地毯，Sn为产生Sm的第n级基本正方形集合，U为平面点集，U的直径|U|＞0，αn（U）表示Sn中与U相交的基本正方形的个数，本文用初等方法证明了对充分大的n有,从而证明了Sm的s-维Hausdorff测度Hs（Sm）＝2s/2．
Let Sm be a Sierpinski carpet with compression ratio 1/m(m≥ 4), Sn be the set of n-th order elementary squares to produce Sm, U be a subset in R2 with diameter |U| > 0. αn.(U) denotes the number of the elementary squares intersecting U in Sn. It will be shown that (s=logm 4) for large n by elementary method, therefore we obtain that , where Hs(Sm) denotes s-dimensional Hausdorff mearsure of Sm.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第4期599-604,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金!19671018
福建省自然科学基金
