Translation properties of sets of positive upper density

Vitaly Bergelson; Benjamin Weiss

doi:10.1090/S0002-9939-1985-0787875-3

Translation properties of sets of positive upper density

Vitaly Bergelson^*, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Generalizing a result of Raimi we show that there exists a set E ⊂ N such that if A ⊂ N is a set with positive upper density, then there exists a number k ∈ N such that d*((A + k) ∩ E) > 0 and d*((A + k) ∩ E^c) > 0. Some extensions and further results are also obtained.

Original language	English
Pages (from-to)	371-376
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	94
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1985-0787875-3
State	Published - Jul 1985

Keywords

Density
Normal number

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10.1090/S0002-9939-1985-0787875-3

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abstract = "Generalizing a result of Raimi we show that there exists a set E ⊂ N such that if A ⊂ N is a set with positive upper density, then there exists a number k ∈ N such that d*((A + k) ∩ E) > 0 and d*((A + k) ∩ Ec) > 0. Some extensions and further results are also obtained.",

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AB - Generalizing a result of Raimi we show that there exists a set E ⊂ N such that if A ⊂ N is a set with positive upper density, then there exists a number k ∈ N such that d*((A + k) ∩ E) > 0 and d*((A + k) ∩ Ec) > 0. Some extensions and further results are also obtained.

KW - Density

KW - Normal number

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Translation properties of sets of positive upper density

Abstract

Keywords

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