Introduction to Measure Theory and Functional Analysis [Paperback]

This book introduces readers to?theories that play a crucial?role in modern mathematics, such as integration and?functional analysis,?employing?a unifying approach that?views?these two subjects as?being?deeply intertwined. This feature is particularly evident?in the broad range of?problems?examined, the solutions?of?which are often supported by generous hints. If the material is split into two courses,?it can be supplemented by?additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures.

This textbook?addresses the needs of?graduate students in mathematics, who will find?the?basic?material they?will need in their future careers, as well as?those of?researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

This is an excellent introductory text on measure theory and integration, with a very good presentation of two fundamental aspects of functional analysis: Hilbert spaces and Banach spaces. The material is presented at a level accessible for a graduate student in mathematics or a researcher in another, related discipline. & Each section contains a large number of examples and exercises accompanied by generous hints. (Victoria R. Steblovskaya, Mathematical Reviews, June, 2016)

This book, written by leading experts, is a well-crafted textbook covering a medley of relevant topics in measure theory and functional analysis in a rather get-to-the-point-quickly fashion, yet resulting in a very readable and enjoyable journey. & The book manages to cover quite a lot of ground in a relatively short number of pages strewn with plenty of exercises. & All-in-all, the student reading this book stands to gain much knowledge, develop anlÓ@