A double return times theorem

Abstract

We prove that for any bounded functions $f_1,f_2$ on a measure-preserving dynamical system $(X,T)$ and any distinct integers $a_1,a_2$, for almost every $x$ the sequence $$f_1(T^{a_{1}n}x)f_2(T^{a_{2}n}x)$$ is a good weight for the pointwise ergodic theorem.

v2: 8 pages, improved typography

References in corpus (1)

• Return times theorem for amenable groups