<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In the classical probability, as well as in the fuzzy probability theory, random events and probability measures are modelled by functions into the closed unit interval [0,1]. Using elementary methods of category theory, we present a classification of the extensions of generalized probability measures (probability measures and integrals with respect to probability measures) from a suitable class of generalized random events to a larger class having some additional (algebraic and/or topological) properties. The classification puts into a perspective the classical and some recent constructions related to the extension of sequentially continuous functions.</p></abstract>

In the classical probability, as well as in the fuzzy probability theory, random events and probability measures are modelled by functions into the closed unit interval [0,1]. Using elementary methods of category theory, we present a classification of the extensions of generalized probability measures (probability measures and integrals with respect to probability measures) from a suitable class of generalized random events to a larger class having some additional (algebraic and/or topological) properties. The classification puts into a perspective the classical and some recent constructions related to the extension of sequentially continuous functions.

Real Functions and the Extension of Generalized Probability Measures

Faculty of Mathematics Physics and Informatics Comenius University Mlynská dolina SK–842-48 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"Real Functions and the Extension of Generalized Probability Measures"}

In the classical probability, as well as in the fuzzy probability theory, random events and probability measures are modelled by functions into the closed unit...

Real Functions and the Extension of Generalized Probability Measures

Published Online: Aug 13, 2013

Page range: 85 - 94

DOI: https://doi.org/10.2478/tmmp-2013-0022

This content is open access.