505 0_ |a 1. Measures -- 2. Functions and integrals -- 3. Convergence -- 4. Signed and complex measures -- 5. Product measures -- 6. Differentiation -- 7. Measures on locally compact spaces -- 8. Polish spaces and analytic sets -- 9. Haar measure -- A. Notation and set theory -- B. Algebra -- C. Calculus and topology in Rd[supercript] -- D. Topological spaces and metric spaces -- E. The Bochner integral -- F. Liftings -- G. The Banach-Tarski paradox -- H. The Henstock-Kurzweil and McShane integrals.

520 3_ |a New edition provides additional topics such as the Kurzweil-Henstock integral, Banach-Tasrki paradox, a proof of the existence of liftings, the Daniell integral, and a brief introduction to measure-theoretic probability theory. Contains numerous examples and exercises. Provides a solid background for study in harmonic analysis and probability theory. Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.