Gd. Richardson et Dc. Kent, PROBABILISTIC CONVERGENCE SPACES, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 61, 1996, pp. 400-420
Citations number
9
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
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.