Introduction to Measure Theory and Functional Analysis

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.

Highlights interaction between integration theory and functional analysis, with constant focus on applications Includes a large number of examples and exercises, often proposed with hints for the reader Self-contained exposition thanks to numerous reminders covered in the appendices Includes supplementary material: sn.pub/extras

Autorentext

Prof. Piermarco Cannarsa, Full professor in Mathematical Analysis, Dept. of Mathematics, Università degli Studi di Roma "Tor Vergata", via della Ricerca Scientifica 1, 00133 Roma, Italy and Italian coordinator of the European Research Group (GDRE) on "Control of Partial Differential Equations" (CONEDP) issued by CNRS, INdAM and Universite' de Provence. Prof. Teresa D'Aprile, Dept. of Mathematics, Università degli Studi di Roma "Tor Vergata", via della Ricerca Scientifica 1, 00133 Roma, Italy

Inhalt
1 Part I Measure and Integration.- 2 Part II Functional Analysis.- 3 Part III Selected Topics.- 4 Appendices.- 5 Index.