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.