Functional analysis deals with infinite-dimensional spaces. Its results are among the greatest achievements of modern mathematics and it has wide-reaching applications to probability theory, statistics, economics, classical and quantum physics, chemistry, engineering, and pure mathematics. This book deals with measure theory and discrete aspects of functional analysis, including Fourier series, sequence spaces, matrix maps, and summability. Based on the author's extensive teaching experience, the text is accessible to advanced undergraduate and first-year graduate students. It can be used as a basis for a one-term course or for a one-year sequence, and is suitable for self-study for readers with an undergraduate-level understanding of real analysis and linear algebra. More than 750 exercises are included to help the reader test their understanding. Key background material is summarized in the Preliminaries.

'Every theorem, proposition, lemma, and corollary has a very understandable proof, is easy to follow, and is well supported by the previous results (in the sense of a self-contained book). … I do not hesitate to say that this book is not far from being an encyclopedic book in functional analysis-measure theory-Fourier series.'

Rigoberto Vera Mendoza Source: MathSciNet (https://mathscinet.ams.org)