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

 

On coverings of convex sets by translates of slabs


Author: H. Groemer
Journal: Proc. Amer. Math. Soc. 82 (1981), 261-266
MSC: Primary 52A45
MathSciNet review: 609663
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Abstract: Let $ ({S_1},{S_2}, \ldots )$ be a sequence of slabs in euclidean $ n$-dimensional space and let $ {t_i}$ denote the thickness of $ {S_i}$. It is shown that the condition $ \sum {t_i^{(n + 1)/2} = \infty } $ implies that every convex set can be covered by translates of the slabs $ {S_i}$, and that the exponent $ (n + 1)/2$ is, in a certain sense, best possible.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0609663-7
PII: S 0002-9939(1981)0609663-7
Article copyright: © Copyright 1981 American Mathematical Society