Overview

Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website.

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9781611977813

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Samopriya Basu is a MITACS Accelerate Postdoctoral Fellow in Statistics at Simon Fraser University, Canada. His research interests include the probabilistic foundations of statistical paradigms and applications to problems in the geophysical sciences and linguistics. He also works on building comparative linguistic databases focusing on under-resourced languages, especially of western North America. Troy Butler is a full professor in the Department of Mathematical and Statistical Sciences at University of Colorado Denver. He served as Associate Chair from 2021 to 2023. He began a tour of duty at the National Science Foundation as a rotating Program Director for Computational Mathematics within the Division of Mathematical Sciences. Don Estep is Director of the Canadian Statistical Sciences Institute and is the Canada Research Chair in Computational Probability and Uncertainty Quantification (Tier 1) in the Department of Statistics and Actuarial Science at Simon Fraser University. He is also a SIAM Fellow. His research interests include uncertainty quantification for complex physics models, stochastic inverse problems, adaptive computation, and modeling of multiscale systems. Don is an avid hiker and cyclist. Nishant Panda is a staff scientist in the Information Sciences Group at Los Alamos National Laboratory. His research involves diverse areas of applied mathematics including artificial intelligence, statistical learning, uncertainty quantification, and numerical analysis. When he is not spooked by bears and coyotes, he enjoys long hikes with his dogs in the picturesque trails of northern New Mexico.

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