Christopher M. Wedrychowicz

Almost everywhere convergence of convolution powers without finite second moment

We generalize a theorem of Bellow and Calderón concerning the a.e. convergence of the convolution powers $\ds μ^nf(x)=\sum_{k}μ^n(k)f(T^k x)$ where $T$ is a measure preserving transformation of a probability space and $μ$ is a probability measure on the integers.