This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text.

Preface
Reader's Guide
List of Figures
List of Tables
Prelude: Random Walks
1 Probability
2 Random Variables
3 Independence
4 Expectation
5 Convergence of Sequences of Random Variables
6 Characteristic Functions
7 Classical Limit Theorems
8 Prediction and Conditional Expectation
9 Martingales
A Notation
B Named Objects
Bibliography
Index

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