Measure Theory

This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs - sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who 'omit 'trivial' steps' and 'make not-so-obvious 'it is obvious' remarks'. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises. Measure theory investigates the conditions under which integration can take place. It considers various ways in which the 'size' of a set can be estimated. This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering. This title is designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra). It includes 140 classical measure-theory problems. It is carefully crafted to present essential elements of the theory in compact form.