Probabilistic Convergence Spaces

    Authors

    G. D. Richardson;D. C. Kent

    Comments

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    Abbreviated Journal Title

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

    Keywords

    probabilistic convergence space; initial probabilistic convergence; structure; probabilistic closure operator; Kowalsky diagonal axiom; Fischer diagonal axiom; Mathematics; Statistics & Probability

    Abstract

    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 Title

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

    Volume

    61

    Publication Date

    1-1-1996

    Document Type

    Article

    Language

    English

    First Page

    400

    Last Page

    420

    WOS Identifier

    WOS:A1996VY88900010

    ISSN

    0263-6115

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