On a problem of Erdős on sequences and measurable sets

Author:
K. J. Falconer

Journal:
Proc. Amer. Math. Soc. **90** (1984), 77-78

MSC:
Primary 28A75; Secondary 11K55

DOI:
https://doi.org/10.1090/S0002-9939-1984-0722418-0

MathSciNet review:
722418

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Abstract: Erdös has conjectured that given a decreasing sequence of real numbers convergent to 0 there always exists a measurable set of positive measure that contains no similar copy of the sequence. We prove this conjecture if the sequence does not converge too rapidly.

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DOI:
https://doi.org/10.1090/S0002-9939-1984-0722418-0

Article copyright:
© Copyright 1984
American Mathematical Society