Real analysis

This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to introduce topics and to illustrate important concepts. KEY TOPICS: Explains the ideas behind developments and proofs -- showing that proofs come not from “ magical methods” but from natural processes. Introduces concepts in stages, and features applications of abstract theorems to concrete settings -- showing the power of an abstract approach in problem solving. Intended for beginning graduate-level courses in Real Analysis, Measure Theory, Lebesque Integration, and Functional Analysis. This book presents the tools, methods and history of analysis. It includes examples and exercises to illustrate and motivate the concepts.