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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The measure of the intersection of rotates of a set on the circle


Author: Wolfgang M. Schmidt
Journal: Proc. Amer. Math. Soc. 48 (1975), 18-20
DOI: https://doi.org/10.1090/S0002-9939-1975-0357343-5
MathSciNet review: 0357343
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Abstract | Additional Information

Abstract: Let $ S$ be a set of real numbers modulo 1 of Lebesgue measure less than 1. It is shown that for every $ \epsilon > 0$ and for large $ k$, there exist translates $ S + {y_1}, \cdots ,S + {y_k}$ of $ S$ such that the measure of their intersection is less than $ {\epsilon^k}$.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357343-5
Keywords: Numbers modulo 1, measure, translates
Article copyright: © Copyright 1975 American Mathematical Society

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