PROBABILISTIC CONVERGENCE SPACES

A basic theory for probabilistic convergence spaces based on filter co nvergence is introduced. As in Florescu's previous theory of probabili stic convergence structures based on nets, one is able to assign a pro bability that a given filter converges to a given point. Various conce pts and theorems pertaining to convergence spaces are extended to the realm of probabilistic convergence spaces, and illustrated by means of examples based on convergence in probability and convergence almost e verywhere. Diagonal axioms due to Kowalsky and Fischer are also studie d, first for convergence spaces and then in the setting of probabilist ic convergence spaces.