A visit to the Erdös problem
Paul D. Humke, Miklós Laczkovich · Proceedings of the American Mathematical Society · 1998
Erdős asked if for every infinite set, A A , of real numbers there exists a measurable subset of the reals having positive measure that does not contain a subset similar to A 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.