Classical in its approach, this textbook is thoughtfully designed and
composed in two parts. Part I is meant for a one-semester beginning
graduate course in measure theory, proposing an "abstract" approach to
measure and integration, where the classical concrete cases of Lebesgue
measure and Lebesgue integral are presented as an important particular
case of general theory. Part II of the text is more advanced and is
addressed to a more experienced reader. The material is designed to
cover another one-semester graduate course subsequent to a first course,
dealing with measure and integration in topological spaces.
The final section of each chapter in Part I presents problems that are
integral to each chapter, the majority of which consist of auxiliary
results, extensions of the theory, examples, and counterexamples.
Problems which are highly theoretical have accompanying hints. The last
section of each chapter of Part II consists of Additional Propositions
containing auxiliary and complementary results. The entire book contains
collections of suggested readings at the end of each chapter in order to
highlight alternate approaches, proofs, and routes toward additional
results.
With modest prerequisites, this text is intended to meet the needs of a
contemporary course in measure theory for mathematics students and is
also accessible to a wider student audience, namely those in statistics,
economics, engineering, and physics. Part I may be also accessible to
advanced undergraduates who fulfill the prerequisites which include an
introductory course in analysis, linear algebra (Chapter 5 only), and
elementary set theory.
