#### Title

T-regular probabilistic convergence spaces

#### Abbreviated Journal Title

J. Aust. Math. Soc. A-Pure Math. Stat.

#### Keywords

convergence space; probabilistic convergence space; T-regular space; Mathematics; Statistics & Probability

#### Abstract

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 Title

Journal of the Australian Mathematical Society Series a-Pure Mathematics and Statistics

#### Volume

64

#### Publication Date

1-1-1998

#### Document Type

Article

#### Language

English

#### First Page

210

#### Last Page

221

#### WOS Identifier

#### ISSN

0263-6115

#### Recommended Citation

"T-regular probabilistic convergence spaces" (1998). *Faculty Bibliography 1990s*. 2364.

https://stars.library.ucf.edu/facultybib1990/2364

## Comments

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