Bourgain's $L^2$ pointwise ergodic theorem over function fields

Thái Hoà ng Lê, Andrew Lott

We prove a function-field analogue of Bourgain's $L^2$ pointwise ergodic theorem. Let $q$ be a power of a prime $p$, let ${\mathbb{F}}_q[t]$ be the ring of polynomials over the finit…