This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure the

Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior

This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.

Apart from new examples and exercises, some simplifications of proofs, minor improvements, and correction of typographical errors, the principal change from the

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales,