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