DOUBLING MEASURES ON CANTOR SETS AND THEIR EXTENSIONS

被引：7
|
作者：
Wang, X. H. [2 ,3 ]
Wen, S. Y. [1 ]
机构：
[1] Hubei Univ, Dept Math, Wuhan 430062, Peoples R China
[2] Cent Univ Finance & Econ, China Econ & Management Acad, Beijing 100081, Peoples R China
[3] Shenzhen Univ, Inst Adv Study, Shenzhen 518060, Peoples R China
来源：
ACTA MATHEMATICA HUNGARICA | 2012年 / 134卷 / 04期
关键词：
middle interval Cantor set; binomial measure; doubling measure; WHITNEY MODIFICATION SETS; NONEXISTENCE;
D O I：
10.1007/s10474-011-0186-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the doubling property of binomial measures on the middle interval Cantor set. We obtain a necessary and sufficient condition that enables a binomial measure to be doubling. Then we determine those doubling binomial measures which can be extended to be doubling on [0, 1]. Finally, we construct a compact set X in [0, 1] and a doubling measure mu on X, such that (F) over bar (X) = X and mu|(EX) is doubling on E-X, where E-X is the set of accumulation points of X and F-X is the set of isolated points of X.
引用
收藏
页码：431 / 438
页数：8
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