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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 a covering property of convex sets
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by H. Groemer PDF
Proc. Amer. Math. Soc. 59 (1976), 346-352 Request permission

Abstract:

Let $\{ {K_1},\;{K_2}, \ldots \}$ be a class of compact convex subsets of euclidean $n$-space with the property that the set of their diameters is bounded. It is shown that the sets ${K_i}$ can be rearranged by the application of rigid motions so as to cover the total space if and only if the sum of the volumes of all the sets ${K_i}$ is infinite. Also, some statements regarding the densities of such coverings are proved.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 346-352
  • MSC: Primary 52A45
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0412970-2
  • MathSciNet review: 0412970