This text investigates the foundational principles of probability and measure theory, essential for advanced study in statistics and related fields. The book is designed for a graduate-level course, providing rigorous coverage of core concepts. It builds upon essential background topics in analysis to explore conditional probability, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion. The author assumes a solid mathematical background from the reader.

This text is regarded as a standard graduate-level reference for probability and measure theory. Its comprehensive coverage of advanced topics makes it a valuable resource for students and researchers in mathematics and statistics. The rigorous approach and detailed explanations ensure a deep understanding of the subject matter. The book is particularly noted for its thorough treatment of martingales and Brownian motion.