A strong-type Furstenberg-Sárközy theorem for sets of positive measure

Polona Durcik, Vjekoslav Kovač, Mario Stipčić

For every $\beta \in (0,\infty )$, $\beta \ne 1$ we prove that a positive measure subset $A$ of the unit square contains a point $(x_0,y_0)$ such that $A$ nontrivially intersects curves $y-y_…