科研之友
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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.
