Foundations of Constructive Probability Theory

This text gives a systematic, detailed constructive theory of probability theory, in the sense of Bishop's constructive mathematics. It is accessible to beginning graduate students with no prior training in constructive mathematics or probability theory and will interest readers in either discipline, as well as those interested in the intersection.

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Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.