正四面体生成的Sierpinski海绵的Hausdorff测度

华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (1): 37-43.

正四面体生成的Sierpinski海绵的Hausdorff测度

陈映洲^1_,桂咏新^2_, 李文侠¹

1. 华东师范大学数学系, 上海, 200062; 2. 咸宁学院数学系, 湖北咸宁, 437005;

收稿日期:2007-03-05 修回日期:2007-05-25 出版日期:2008-01-25 发布日期:2008-01-25
通讯作者: 李文侠

Hausdorff measure of Sierpinski Sponge generated by normal tetrahedron(Chinese)

CHEN Ying-zhou¹, GUI Yong-xin², LI Wen-xia¹

1. Department of Mathematics, East China Normal University, Shanghai 200062, China; 2. Department of Mathematics, Xianning College, Xianning Hubei, 437005, China;

Received:2007-03-05 Revised:2007-05-25 Online:2008-01-25 Published:2008-01-25
Contact: LI Wen-xia

摘要/Abstract

摘要： 研究了一类由迭代函数系统生成的自相似集的Hausdorff测度，在压缩比满足一定条件下，通过确定其最大上凸密度得到此类正四面体Sierpinski海绵的Hausdorff测度的精确值为1。

关键词: 自相似集, Hausdorff测度, 上凸密度, 自相似集, Hausdorff测度, 上凸密度

Abstract: In this paper, the Hausdorff measure of a class of self-similar sets in ${\mathbf R}^3$ is considered. The exact Hausdorff measures of those sets are obtained under some conditions.

Key words: Hausdorff measure, upper convex density, self-similar set, Hausdorff measure, upper convex density

中图分类号:

O174.12

陈映洲_; 桂咏新_; 李文侠. 正四面体生成的Sierpinski海绵的Hausdorff测度[J]. 华东师范大学学报(自然科学版), 2008, 2008(1): 37-43.

CHEN Ying-zhou;GUI Yong-xin;LI Wen-xia. Hausdorff measure of Sierpinski Sponge generated by normal tetrahedron(Chinese)[J]. Journal of East China Normal University(Natural Sc, 2008, 2008(1): 37-43.