Notes on Constructive Probability Theory

Abstract

This paper is part of the constructive program, initiated by E. Bishop, of systematic examination of classical mathematics for their computational content. From this constructive standpoint, basic concepts in probability theory are studied. Positive proofs are then given to some important theorems: Ionescu-Tulcea's theorem, a submartingale convergence theorem, and the construction of a Markov process from a strongly continuous semi-group of transition operators.