数学物理学报(英文版) ›› 1999, Vol. 19 ›› Issue (1): 81-85.

• 论文 • 上一篇    下一篇

DIMENSIONS OF MEASURE ON GENERAL SIERPINSKI CARPET

 LI Wen-Xia, XIAO Dong-Mei   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China
  • 收稿日期:1997-01-27 出版日期:1999-03-02 发布日期:1999-03-02
  • 基金资助:

    Supported by a grant from the National Science Foundation of China

DIMENSIONS OF MEASURE ON GENERAL SIERPINSKI CARPET

 李文侠, 肖冬梅   

  1. Department of Mathematics, Central China Normal University, Wuhan 430079, China
  • Received:1997-01-27 Online:1999-03-02 Published:1999-03-02
  • Supported by:

    Supported by a grant from the National Science Foundation of China

PDF (PC)

1006

摘要：

Let S =
Q1
i=1{0, 1, · · · , r − 1} and ¯R the general Sierpinski carpet. Let μ be
the induced probability measure on ¯R of ˜μ on S by , where  is the natural surjection from
S onto ¯R and ˜μ is the infinite product probability measure corresponding to probability
vector (b0, · · · , br−1) with bi = alogn m−1
i /m . Authors show that
dimH μ = CL(μ) = CL(μ) = C(μ) = C(μ) = .

关键词: General Sierpinski carpet, dimension of measure, probability measure

Abstract:

Let S =
Q1
i=1{0, 1, · · · , r − 1} and ¯R the general Sierpinski carpet. Let μ be
the induced probability measure on ¯R of ˜μ on S by , where  is the natural surjection from
S onto ¯R and ˜μ is the infinite product probability measure corresponding to probability
vector (b0, · · · , br−1) with bi = alogn m−1
i /m . Authors show that
dimH μ = CL(μ) = CL(μ) = C(μ) = C(μ) = .

Key words: General Sierpinski carpet, dimension of measure, probability measure

中图分类号: 

  • 28A80
版权所有 © 《数学物理学报(英文版)》杂志社
地址：武汉市71010号信箱(430071)　电话: 027-87199206(中文版)　027-87199087(英文版)
E-mail: actams@apm.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发