Almost everywhere convergence of convolution measures.

摘要

Let (X, B, m, tau) be a dynamical system with (X, B, m) a probability space and tau a measurable, invertible, measure preserving transformation. The present thesis deals with the almost everywhere convergence in L1(X) of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are convolution products of members of a sequence of probability measures {nui} on Z. In the last section, we also prove a variation inequality for this type of sequence operators.