Foundations of Constructive Probability Theory

Reviews / Votes

'After decades out of academia, Chan (a highly talented doctoral student of Errett Bishop's) has returned to the fold with this massive volume of mostly original, and highly valuable, research on constructive probability and measure theory. His book should be the definitive reference for Bishop-style work on those aspects of analysis for the foreseeable future. I cannot recommend it highly enough.' Douglas Bridges, University of Canterbury 'Foundations of Constructive Probability Theory extends the range of constructive mathematics to the arena of probability theory. It can well serve as a parallel introduction into constructive mathematics and rigorous probability theory. It can be challenging to traditional mathematicians to give up the proof of existence of mathematical objects by proving that the assumed nonexistence leads to a contradiction, without ever having shown a construction of the actual object. The treatment of the book is at the highest measure-theoretic level using the Daniell integral approach, covering many basic topics such as random variables, probability distributions, weak convergence, independence and conditional expectations, and the Central Limit Theorem. This is followed by a broad range of topics in stochastic processes. It will also serve well as a foundation of further research in that area.' Fritz Scholz, University of Washington 'The definitive work on constructive probability by Errett Bishop's most talented student. Classical probability theory is treated in a computational way while focusing on the mathematics.' Fred Richman, Florida Atlantic University 'This book is an important contribution to Bishop-style constructive mathematics (BISH), as it offers an elaborate development of constructive probability theory within Bishop-Cheng Measure Theory (BCMT).' Iosif Petrakis, zbMATH