Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On packing measures and a theorem of Besicovitch
HTML articles powered by AMS MathViewer

by Ignacio Garcia and Pablo Shmerkin PDF
Proc. Amer. Math. Soc. 142 (2014), 2661-2669 Request permission

Abstract:

Let $\mathcal {H}^h$ be the $h$-dimensional Hausdorff measure on $\mathbb {R}^d$. Besicovitch showed that if a set $E$ is null for $\mathcal {H}^h$, then it is null for $\mathcal {H}^g$, for some dimension $g$ smaller than $h$. We prove that this is not true for packing measures. Moreover, we consider the corresponding questions for sets of non-$\sigma$-finite packing measure and for pre-packing measure instead of packing measure.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 28A78, 28A80
  • Retrieve articles in all journals with MSC (2010): 28A78, 28A80
Additional Information
  • Ignacio Garcia
  • Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Mar del Plata, Buenos Aires Province, Argentina
  • Email: nacholma@gmail.com
  • Pablo Shmerkin
  • Affiliation: Department of Mathematics, Faculty of Engineering and Physical Sciences, University of Surrey, Guilford, GU2 7XH, United Kingdom
  • Address at time of publication: Torcuato Di Tella University, Av. Figeroa Alcorta 7350 (1428), Buenos Aires, Argentina
  • MR Author ID: 781925
  • Email: pshmerkin@utdt.edu
  • Received by editor(s): May 28, 2012
  • Received by editor(s) in revised form: July 24, 2012
  • Published electronically: April 24, 2014
  • Additional Notes: The first author was partially supported by CAI+D2009 No. 62-310 (Universidad Nacional del Litoral) and E449 (UNMDP)
    The second author was partially supported by a Leverhulme Early Career Fellowship and by a Cesar Milstein Grant
    The authors thank the referee for helpful comments
  • Communicated by: Tatiana Toro
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2661-2669
  • MSC (2010): Primary 28A78; Secondary 28A80
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11962-9
  • MathSciNet review: 3209322