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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Ultrametrics and geometric measures


Authors: H. Movahedi-Lankarani and R. Wells
Journal: Proc. Amer. Math. Soc. 123 (1995), 2579-2584
MSC: Primary 54E40; Secondary 28A75, 54E35
DOI: https://doi.org/10.1090/S0002-9939-1995-1307552-6
MathSciNet review: 1307552
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Abstract: Let Z be a locally connected, locally compact, and separable metric space equipped with a geometric measure v. It is shown that if a subset Y of Z is bi-Lipschitz isomorphic to an ultrametric space, then $ \nu (Y) = 0$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1307552-6
Keywords: Lipschitz, ultrametric, geometric measure, Lebesgue measure, logarithmic ratio, Hausdorff dimension, metric dimension
Article copyright: © Copyright 1995 American Mathematical Society