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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On uniform properties of doubling measures
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by Michael Ruzhansky PDF
Proc. Amer. Math. Soc. 129 (2001), 3413-3416 Request permission

Abstract:

In this paper we prove that if $(X,d,\mu )$ is a metric doubling space with segment property, then $\inf r(E)/r(B)>0$ if and only if $\inf \mu (E)/\mu (B)>0$, where the infimum is taken over any collection $\mathcal {C}$ of balls $E, B$ such that $E\subset B\subset X$. As a consequence we show that if $X$ is a linear metric doubling space, then it must be finite dimensional.
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Additional Information
  • Michael Ruzhansky
  • Affiliation: Department of Mathematics and Statistics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom
  • Address at time of publication: Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, England
  • MR Author ID: 611131
  • Email: ruzh@maths.ed.ac.uk, ruzh@ic.ac.uk
  • Received by editor(s): November 23, 1999
  • Received by editor(s) in revised form: March 24, 2000
  • Published electronically: May 3, 2001
  • Communicated by: Christopher D. Sogge
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3413-3416
  • MSC (2000): Primary 54E35, 54E50, 46A03, 28E15
  • DOI: https://doi.org/10.1090/S0002-9939-01-05931-7
  • MathSciNet review: 1845020