Di Nola, Lapenta and Lenzi
A point-free approach to measurability and statistical models
In this work we approach the problem of finding the most natural algebraic structure of the set of all possible random variables on a measurable space, inspired by Nelson's point of view. We build our work on previous papers by the same authors and set our investigation in the framework of MV-algebras and algebraic logic. We approach the problem from the perspective of pointfree topology, in order to take the notion of random variable as the primitive one. In the final part of the paper we approach statistical models from the point of view of algebra and category theory, providing a different and perhaps more insightful justification for our logico-algebraic approach to the notion.