Almost everywhere convergence of convolution powers without finite second moment

Abstract

We generalize a theorem of Bellow and Calder\'on concerning the a.e. convergence of the convolution powers \ds \mu^nf(x)=\sum_{k}\mu^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.Comment: 13 pages, to appear in Annales de l Institut Fourie