Tauberian theorems via statistical convergence

The concept of statistical convergence, which is related to the usual conce pt of convergence in probability, provides a regular summability method for abstract metric spaces. By using probabilistic tools, we provide some Taub erian theorems which have best possible order Tauberian conditions. Further more, these methods can be used to unify and improve the classical pointwis e Tauberian theorems of summability theory for the random walk type methods as proved by Bingham, and Hausdorff methods as proved by Lorentz. (C) 1998 Academic Press.