<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We continue our study of the extensions of generalized probability measures. First, we describe some extensions of generalized random events (represented by classes of functions with values in [0,1]) to which generalized probability measures can be extended. Second, we study products of domains of probability and describe states on such products. Third, we show that the events in IF-probability, introduced by B. Riečan, form a suitable category isomorphic to a subcategory of the category of fuzzy random events. Consequently, IF-probability can be interpreted within fuzzy probability theory. We put forward some problems related to the extensions of probability domains and hint some applications.</p></abstract>

We continue our study of the extensions of generalized probability measures. First, we describe some extensions of generalized random events (represented by classes of functions with values in [0,1]) to which generalized probability measures can be extended. Second, we study products of domains of probability and describe states on such products. Third, we show that the events in IF-probability, introduced by B. Riečan, form a suitable category isomorphic to a subcategory of the category of fuzzy random events. Consequently, IF-probability can be interpreted within fuzzy probability theory. We put forward some problems related to the extensions of probability domains and hint some applications.

Real functions and the extension of generalized probability measures II

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

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Real functions and the extension of generalized probability measures II"}

We continue our study of the extensions of generalized probability measures. First, we describe some extensions of generalized random events (represented by...

Real functions and the extension of generalized probability measures II

Published Online: Sep 25, 2015

Page range: 191 - 204

Received: Feb 21, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0016

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.