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

Translation properties of sets of positive upper density


Authors: Vitaly Bergelson and Benjamin Weiss
Journal: Proc. Amer. Math. Soc. 94 (1985), 371-376
MSC: Primary 11K16
MathSciNet review: 787875
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Abstract: Generalizing a result of Raimi we show that there exists a set $ E \subset {\mathbf{N}}$ such that if $ A \subset {\mathbf{N}}$ is a set with positive upper density, then there exists a number $ k \in {\mathbf{N}}$ such that $ {d^ * }((A + k) \cap E) > 0$ and $ {d^ * }((A + k) \cap {E^c}) > 0$. Some extensions and further results are also obtained.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787875-3
PII: S 0002-9939(1985)0787875-3
Keywords: Density, normal number
Article copyright: © Copyright 1985 American Mathematical Society