Probability and Measure (Wiley Series in Probability and Statistics)

A senior-graduate level text and reference that links the disciplines of probability and measure theory. Including many practical problems and examples, it begins with an introduction to Borel's normal number theorem, proved by calculus alone, followed by short sections that establish the existence and fundamental properties of probability measures, including Lebesque measure on the unit interval. Coverage includes topics in measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes.