Probabilistic Convergence Spaces
Abbreviated Journal Title
J. Aust. Math. Soc. A-Pure Math. Stat.
probabilistic convergence space; initial probabilistic convergence; structure; probabilistic closure operator; Kowalsky diagonal axiom; Fischer diagonal axiom; Mathematics; Statistics & Probability
A basic theory for probabilistic convergence spaces based on filter convergence is introduced. As in Florescu's previous theory of probabilistic convergence structures based on nets, one is able to assign a probability that a given filter converges to a given point. Various concepts 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 everywhere. Diagonal axioms due to Kowalsky and Fischer are also studied, first for convergence spaces and then in the setting of probabilistic convergence spaces.
Journal of the Australian Mathematical Society Series a-Pure Mathematics and Statistics
"Probabilistic Convergence Spaces" (1996). Faculty Bibliography 1990s. 1734.