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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hausdorff dimension and doubling measures
on metric spaces


Author: Jang-Mei Wu
Journal: Proc. Amer. Math. Soc. 126 (1998), 1453-1459
MSC (1991): Primary 28C15; Secondary 54E35, 54E45
MathSciNet review: 1443418
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Abstract | References | Similar Articles | Additional Information

Abstract: Vol$'$berg and Konyagin have proved that a compact metric space carries a nontrivial doubling measure if and only if it has finite uniform metric dimension. Their construction of doubling measures requires infinitely many adjustments. We give a simpler and more direct construction, and also prove that for any $\alpha > 0$, the doubling measure may be chosen to have full measure on a set of Hausdorff dimension at most $\alpha $.


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Additional Information

Jang-Mei Wu
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04317-2
PII: S 0002-9939(98)04317-2
Keywords: Doubling measure, metric space, Hausdorff dimension
Received by editor(s): October 24, 1996
Additional Notes: Partially supported by the National Science Foundation
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society