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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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A function whose graph has positive doubling measure
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by Tuomo Ojala and Tapio Rajala PDF
Proc. Amer. Math. Soc. 144 (2016), 733-738 Request permission

Abstract:

We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen posed in a 2013 paper. Moreover, we show that the doubling constant of the measure can be chosen to be arbitrarily close to the doubling constant of the Lebesgue measure.
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Additional Information
  • Tuomo Ojala
  • Affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35 (MaD), FI-40014 University of Jyvaskyla, Finland
  • MR Author ID: 908269
  • Email: tuomo.j.ojala@jyu.fi
  • Tapio Rajala
  • Affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35 (MaD), FI-40014 University of Jyvaskyla, Finland
  • MR Author ID: 838027
  • Email: tapio.m.rajala@jyu.fi
  • Received by editor(s): January 28, 2015
  • Received by editor(s) in revised form: February 3, 2015
  • Published electronically: June 30, 2015
  • Communicated by: Jeremy Tyson
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 733-738
  • MSC (2010): Primary 28A12; Secondary 30L10
  • DOI: https://doi.org/10.1090/proc12748
  • MathSciNet review: 3430849