Introduction to Measure Theory and Functional Analysis

This book introduces readers totheories that play a crucialrole in modern mathematics, such as integration andfunctional analysis,employinga unifying approach thatviewsthese two subjects asbeingdeeply intertwined. This feature is particularly evidentin the broad range ofproblemsexamined, the solutionsofwhich are often supported by generous hints. If the material is split into two courses,it can be supplemented byadditional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures. This textbookaddresses the needs ofgraduate students in mathematics, who will findthebasicmaterial theywill need in their future careers, as well asthose ofresearchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.