On a Problem of Erdos on Sequences and Measurable Sets

K. J. Falconer
1984 Proceedings of the American Mathematical Society  
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.
doi:10.2307/2044671 fatcat:moadskkibvftrebwdglfll6nre