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Translates of Sequences in Sets of Positive Measure

Published online by Cambridge University Press:  20 November 2018

D. Borwein  and
S. Z. Ditor
D. Borwein
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9
S. Z. Ditor
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9
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Given a measurable set A of real numbers with measure mA > 0, and a sequence {dn} of real numbers converging to zero, is there always an x such that x + dn ∈ A for all n sufficiently large?

The answer to this question, which was posed to the authors by P. Erdös, is NO.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 497 - 498
Copyright
Copyright © Canadian Mathematical Society 1978