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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 the best constant for the Besicovitch covering theorem
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by Zoltán Füredi and Peter A. Loeb PDF
Proc. Amer. Math. Soc. 121 (1994), 1063-1073 Request permission

Abstract:

This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1063-1073
  • MSC: Primary 28A75; Secondary 05B40, 52C17
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1249875-4
  • MathSciNet review: 1249875