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

 

A note on the distance set problem in the plane


Author: Themis Mitsis
Journal: Proc. Amer. Math. Soc. 130 (2002), 1669-1672
MSC (2000): Primary 28A12, 28A78
Published electronically: October 12, 2001
MathSciNet review: 1887013
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Abstract: We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.


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Additional Information

Themis Mitsis
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
Address at time of publication: Nestou 6, Athens 14342, Greece
Email: mitsis@math.jyu.fi, tmitsis@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06375-4
PII: S 0002-9939(01)06375-4
Received by editor(s): November 21, 2000
Published electronically: October 12, 2001
Additional Notes: This research has been supported by a Marie Curie Fellowship of the European Community programme “Improving human potential and the socio-economic knowledge base" under contract number HPMFCT-2000-00442.
Communicated by: David Preiss
Article copyright: © Copyright 2001 American Mathematical Society