Measure And Probability

The book is designed for graduate students and researchers and can serve as material for a two-semester core course on real analysis. The material is mostly about measure and integration over a finite measure space, developing a general mathematical framework for handling uncertainty in quantitative terms, where the probabilistic models for finite and infinite sequence of trials require an understanding of the concept of measure. Most of the topics covered in this book are standard fare, but several proofs of standard theorems are possibly unusual and not too standard, e.g., the strong law of large numbers, the Hahn decomposition of signed measures and the Riesz representation theorem.