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A visit to the Erdos problem

Authors: Paul D. Humke and Miklós Laczkovich
Journal: Proc. Amer. Math. Soc. 126 (1998), 819-822
MSC (1991): Primary 28A99; Secondary 28A05
MathSciNet review: 1425126
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Abstract: Erdos asked if for every infinite set, $A$, of real numbers there exists a measurable subset of the reals having positive measure that does not contain a subset similar to $A$. In this note we transform this question to a finite combinatorial problem. Using this translation we extend some results of Eigen and Falconer concerning slow sequences for which the answer to Erdos' question is positive.

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Additional Information

Paul D. Humke
Affiliation: Department of Mathematics, St. Olaf College, Northfield, Minnesota 55057

Miklós Laczkovich
Affiliation: Department of Analysis, Eötvös Loránd University, Múzeum krt. 6-8, Budapest H-1088, Hungary

Received by editor(s): March 6, 1996
Received by editor(s) in revised form: September 9, 1996
Additional Notes: The first author was supported by the National Research Council of the United States, and the second author by the Hungarian National Foundation for Scientific Research, Grant T016094
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society