Problem 120

Erdős Problem #120: declared status 'open'. Formalized: yes. Let $A\subseteq\mathbb{R}$ be an infinite set. Must there be a set $E\subset \mathbb{R}$ of positive measure which does not contain any set of the shape $aA+b$ for some $a,b\in\mathbb{R}$ and $a\neq 0$? Prize: $100. Tags: combinatorics.