About this article
Published Online: Aug 13, 2013
Page range: 85 - 94
DOI: https://doi.org/10.2478/tmmp-2013-0022
Keywords
extension of probability measures, outer measure, absolutely measurable set, D-poset of fuzzy sets, sequentially continuous D-homomorphism, probability integral, MV -algebra, Łukasiewicz tribe, classification of extensions, ID-extension, epireflective subcategory. Supported in part by the VEGA grant no. 1/0330/13
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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.