Basic Analysis IV:
Measure Theory and Integration
introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides.
Features
• Can be used as a traditional textbook as well as for self-study
• Suitable for advanced students in mathematics and associated disciplines
• Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions