Preface

Probability theory is a fundamental branch of mathematics with applications in numerous fields, including statistics, computer science, physics, and engineering. While the subject has many practical applications, it is also a beautiful and elegant area of mathematics in its own right. This book is designed to offer readers a thorough and rigorous understanding of the concepts and principles that underlie probability theory.

To that end, this book begins with a detailed treatment of measure theory, which provides the mathematical framework for probability theory. I mainly refer to [Taylor and Kingman, 1973] for this part. From there, the book explores the concepts of random variables and distribution functions, and their properties.

Table of Contents

Main Contents

• 1. Measure Theory
  • 1.1. Sum of Countably Many Non-negative Terms
  • 1.2. Classes of Sets
  • 1.3. Set Functions
  • 1.4. Extension of Measures
• 2. Sets and Events
  • 2.1. Probability Spaces
  • 2.2. Distributions

Appendix

• References
• Index