caa a22 4500 388047011 CHVBK 20180307125041.0 cr unu---uuuuu 161130e199804 xx s 000 0 eng 10.1017/S1446788700001701 doi S1446788700001701 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001701 T-regular probabilistic convergence spaces [Elektronische Daten] 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 λ' for several t-norms. Suitable function space structures in terms of a given t-norm are also considered. Copyright © Australian Mathematical Society 1998 primary 54A20 nationallicence 54E70 nationallicence Convergence space nationallicence probabilistic convergence space nationallicence T-regular space nationallicence Minkler J. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address Minkler G. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address Richardson G. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address: garyr@pegasus.cc.ucf.edu Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 210-221 1446-7887 64:2<210 1998 64 JAZ https://doi.org/10.1017/S1446788700001701 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001701 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Minkler J. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address NATIONALLICENCE 700 1- Minkler G. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address NATIONALLICENCE 700 1- Richardson G. Department of Mathematics University of Central Florida Orlando, FL 32816-1364 USA e-mail address: garyr@pegasus.cc.ucf.edu NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 210-221 1446-7887 64:2<210 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge