Introduction to Measure Theory and Functional Analysis

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

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

"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 and hone her skills, and enjoy the trip." (Ittay Weiss, MAA Reviews, maa.org, April, 2016)