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

Generalization of a result of Borwein and Ditor


Author: Harry I. Miller
Journal: Proc. Amer. Math. Soc. 105 (1989), 889-893
MSC: Primary 28A05; Secondary 26A21
MathSciNet review: 989098
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Abstract: D. Borwein and S. Z. Ditor have found a measurable subset $ A$ of the real line having positive Lebesgue measure and a decreasing sequence $ \left( {{d_n}} \right)$ of reals converging to zero such that, for each $ x,x + {d_n}$ is not in $ A$ for infinitely many $ n$; thus answering a question of P. Erdös. It will be shown that the result of Borwein and Ditor can be extended using a general $ 2$-place function in place of plus. Related material is also presented.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0989098-5
PII: S 0002-9939(1989)0989098-5
Article copyright: © Copyright 1989 American Mathematical Society