T-regular probabilistic convergence spaces
Abbreviated Journal Title
J. Aust. Math. Soc. A-Pure Math. Stat.
convergence space; probabilistic convergence space; T-regular space; Mathematics; Statistics & Probability
A probabilistic convergence structure assigns a probability that a given filter converges to a given element of the space. The role of the t-norm (triangle norm) in the study of regularity of probabilistic convergence spaces is investigated. Given a probabilistic convergence space, there exists a finest T-regular space which is coarser than the given space, and is referred to as the 'T-regular modification'. Moreover, for each probabilistic convergence space, there is a sequence of spaces, indexed by nonnegative ordinals, whose first term is the given space and whose last term is its T-regular modification. The T-regular modification is illustrated in the example involving 'convergence with probability lambda' for several t-norms. Suitable function space structures in terms of a given t-norm are also considered.
Journal of the Australian Mathematical Society Series a-Pure Mathematics and Statistics
"T-regular probabilistic convergence spaces" (1998). Faculty Bibliography 1990s. 2364.