Code: 20134

Doubling Measures on Generalized Cantor Sets

Peng sun, Xiaohua Wang

 

Abstracts

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