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

 

On the existence of doubling measures with certain regularity properties


Authors: Per Bylund and Jaume Gudayol
Journal: Proc. Amer. Math. Soc. 128 (2000), 3317-3327
MSC (2000): Primary 28C15; Secondary 54E45, 54F45
Published electronically: May 11, 2000
MathSciNet review: 1676303
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Abstract:

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.


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Additional Information

Per Bylund
Affiliation: Department of Mathematics, University of Umeå, S-90187 Umeå, Sweden
Email: Per.Bylund@math.umu.se

Jaume Gudayol
Affiliation: Departament de Matèmatica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Email: gudayol@mat.ub.es

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05405-8
PII: S 0002-9939(00)05405-8
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: January 4, 1999
Published electronically: May 11, 2000
Additional Notes: The second author is partially supported by MEC grant PB95-0956-C02-01 and CIRIT grant GRQ94-2014.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society