Acta mathematica scientia, Series B >
DOUBLING MEASURES ON GENERALIZED CANTOR SETS
Received date: 2012-08-13
Revised date: 2013-01-10
Online published: 2013-11-20
Supported by
Peng SUN is supported by NSFC (11101447), Xiaohua WANG is supported by NSFC (11201500).
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
SUN Peng , WANG Xiao-Hua . DOUBLING MEASURES ON GENERALIZED CANTOR SETS[J]. Acta mathematica scientia, Series B, 2013 , 33(6) : 1551 -1560 . DOI: 10.1016/S0252-9602(13)60103-4
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