A visit to the Erdös problem
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- by Paul D. Humke and Miklós Laczkovich PDF
- Proc. Amer. Math. Soc. 126 (1998), 819-822 Request permission
Abstract:
Erdős 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 Erdős’ question is positive.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 819-822
- MSC (1991): Primary 28A99; Secondary 28A05
- DOI: https://doi.org/10.1090/S0002-9939-98-04167-7
- MathSciNet review: 1425126