A Basic Course in Probability Theory

A lively book that is a pleasure to read, this work gives analysts the tools to construct Brownian motion from scratch. It includes a complete overview of basic measure theory as well as analysis with proofs.

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Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.