Doubling measures on Cantor sets and their extensions |
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Authors: | Xiaohua Wang Shengyou Wen |
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Institution: | 1.China Economics and Management Academy,Central University of Finance and Economics,Beijing,China;2.Institute for Advanced Study,Shenzhen University,Shenzhen,China;3.Department of Mathematics,Hubei University,Wuhan,China |
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Abstract: | 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 μ on X, such that `(F)]X=X\overline{F}_{X}=X and m|EX{\mu|}_{E_{X}} 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. |
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Keywords: | |
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