Foundations of probability: topological and categorical methods
by
Roman Frič
Mathematical Institute, Slovak Academy of Sciences, Kosice, Slovak Republic

Each Boolean Algebra is isomorphic to a reduced field of subsets and this fact is often used in the foundations of probability theory. The corresponding duality between Boolean algebras and perfect reduced fields is not exactly what is needed. On the one hand, perfectness of the domain guarantees that each Boolean homomorphism is induced by a measurable map. On the other hand, perfectness amounts to compactness and hence each additive probability becomes sigma-additive. We show that a weaker notion of s-perfectness maintains the former and avoids the latter property. The corresponding category of s-perfect fields carrying the usual sequential convergence (equivalent to the pointwise convergence of characteristic functions) is dual to the category whose objects are Boolean algebras carrying a naural sequential convergence and whose morphisms are sequentially continuous Boolean homomorphisms. Further, the construction of the generated sigma-field yields an epireflector prese rving s-perfectness and matching the duality.

Date received: June 27, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-26.