数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (6): 1551-1560.doi: 10.1016/S0252-9602(13)60103-4

• 论文 • 上一篇    下一篇

DOUBLING MEASURES ON GENERALIZED CANTOR SETS

孙鹏1|王小华1,2   

  1. 1. China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, China； 2. Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
  • 收稿日期:2012-08-13 修回日期:2013-01-10 出版日期:2013-11-20 发布日期:2013-11-20
  • 基金资助:

    Peng SUN is supported by NSFC (11101447), Xiaohua WANG is supported by NSFC (11201500).

DOUBLING MEASURES ON GENERALIZED CANTOR SETS

 SUN Peng1, WANG Xiao-Hua1,2   

  1. 1. China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, China； 2. Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
  • Received:2012-08-13 Revised:2013-01-10 Online:2013-11-20 Published:2013-11-20
  • Supported by:

    Peng SUN is supported by NSFC (11101447), Xiaohua WANG is supported by NSFC (11201500).

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摘要：

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.

关键词: Cantor set, binomial measure, doubling measure

Abstract:

We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.

Key words: Cantor set, binomial measure, doubling measure

中图分类号: 

  • 28A80
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