Product sets in sets of returns and positivity of symmetric ergodic averages

Vitaly Bergelson, Saúl Rodríguez-Martín

We study sets of (measurable) returns in countable groups $G$, namely sets of the form $\{g\in G:\mu (A\cap T_{g}A)>0\}$ arising from measure-preserving actions. Extending a result of B…