Almost everywhere convergence of convolution powers without finite second moment

Abstract

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 $\mu$ is a probability measure on the integers.

13 pages, to appear in Annales de l Institut Fourier