Real functions and the extension of generalized probability measures

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.