On a Class of Universal Probability Spaces

Abstract

Aims/ Objectives: The objective of this paper is to introduce a class of probability spaces that include several exceptions introduced by Dieudonn´e [3], Anderson and Jessen [4], and Doob and Jessen [5]. The class of alternative probability space is called the Universal Probability Space (UPS). The UPS consists of Borel sets, elements of which are tensors. It is proven that indeed such tensor sets represent a more general probability space. Given the properties of tensors, it is shown that the exceptions introduced by Dieudonn´ e, Anderson, Jessen, and Doob are merely special events that can occur in the UPS. Study Design: Methodological study. Place and Duration of Study: Research Unit of Economics Traffic Clinic - ETC, Paris, France, between June 2015 and September 2015. Methodology: Borel tensor sets were used in constructing a more general probability space. Results: Some basic definitions and properties of Borel tensor sets in the context of the UPS are given. It is shown that the UPS has a defined metric. Some elements of the UPS are given such as conditional probability and independence property. Conclusion: The UPS is a more generalized probability space.