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 | References | Similar Articles | Additional Information

Abstract: Erdos asked if for every infinite set, , of real numbers there exists a measurable subset of the reals having positive measure that does not contain a subset similar to . 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

Email:
humke@stolaf.edu

**Miklós Laczkovich**

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

Email:
laczk@cs.elte.hu

DOI:
https://doi.org/10.1090/S0002-9939-98-04167-7

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