A Generalized Measure and Probability Theory for the Physical Sciences

Abstract

It is argued that a reformulation of classical measure and probability theory is necessary if the theory is to accurately describe the measurements of physical phenomena. The postulates of a generalized theory are given, the fundamentals of this theory are developed and possible applications and open questions are discussed. Specifically, generalized measure and probability spaces are defined, integration theory is considered, the partial order structure is studied and applications to hidden variables and the logic of quantum mechanics are given.