一个广义Sierpinski地毯的Hausdorff测度

数学季刊 ›› 2003, Vol. 18 ›› Issue (1): 57-67.

一个广义Sierpinski地毯的Hausdorff测度

College of Mathematics and Information Science,Henan Normal University,Xinxiang 453002,China

收稿日期:2001-11-01 出版日期:2003-03-30 发布日期:2024-04-22
作者简介:CUI Zhen-wen（1942－）,male,native of Nanjing,Jiangsu,a professor of Henan Normal University ,engages in fractal theory with applications and approximation theory with applications．
基金资助:
Supported by the National Natural Science Foundation of China（69874010）

The Hausdorff Measure of a Generalized Sierpinski Carpet

College of Mathematics and Information Science,Henan Normal University,Xinxiang 453002,China

Received:2001-11-01 Online:2003-03-30 Published:2024-04-22
About author:CUI Zhen-wen（1942－）,male,native of Nanjing,Jiangsu,a professor of Henan Normal University ,engages in fractal theory with applications and approximation theory with applications．
Supported by:
Supported by the National Natural Science Foundation of China（69874010）

摘要/Abstract

摘要： In this paper,first ,we prove that the Sierpinski carpet E is equivalent to the set R ．Then we define a mass distribution on R ．Using a certain of mass distribution,we obtain the lower bound about the Hausdorff measure of R ．Therefore the exact value of Hausdorff measure of E is given．

关键词: fractal, Hausdorff measure, Sierpinski carpet

Abstract: In this paper,first ,we prove that the Sierpinski carpet E is equivalent to the set R ．Then we define a mass distribution on R ．Using a certain of mass distribution,we obtain the lower bound about the Hausdorff measure of R ．Therefore the exact value of Hausdorff measure of E is given．

Key words: fractal, Hausdorff measure, Sierpinski carpet

中图分类号:

O174．12

崔振文, 杨永琴, 王彩芬. 一个广义Sierpinski地毯的Hausdorff测度[J]. 数学季刊, 2003, 18(1): 57-67.

CUI Zhen-wen, YANG Yong-qin, WANG Cai-fen. The Hausdorff Measure of a Generalized Sierpinski Carpet[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(1): 57-67.

[1]	张云秀, 顾惠. 一类Sierpinski垫片的Hausdorff测度的估计[J]. 数学季刊, 2012, 27(1): 59-62.
[2]	曾超益. 广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明[J]. 数学季刊, 2006, 21(2): 293-296.