科研之友
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摘要
We study the doubling property of measures on self-affine carpets of Bedford and McMullen. Let M be the family of such carpets, and let S is an element of M be a given carpet. We obtain an equivalent condition for a Borel measure to be doubling on S, and then consider self-affine measures on the carpet S. We encounter several cases; in each one, we obtain a complete characterization for doubling self-affine measures on S. In contrast with the fact that every self-similar carpet carries a doubling self similar measure, we found that there are self-affine carpets in M that do not carry any doubling self-affine measure. We give a geometric characterization for those "good" carpets.
