On an Erdős similarity problem in the large

Xiang Gao, Yuveshen Mooroogen, Chi Hoi Yip

In a recent paper, Kolountzakis and Papageorgiou ask if for every $\hat{I}\mu \in (0,1]$, there exists a set $S\subseteq \mathbb{R}$ such that $|S\cap I|\ge 1-\hat{I}\mu$ for every i…