Random Sequences and Pointwise Convergence of Multiple Ergodic Averages

Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl

We prove pointwise convergence, as $N\to \infty$, for the multiple ergodic averages $\frac{1}{N}{\sum }_{n=1}^{N}f(T^{n}x)\cdot g(S^{a_n}x)$, where $T$ and $S$ are commuting measure pres…