Point Set Topology, Banach and Hilbert Space, Measure Theory, Fourier Series and Transforms, Distribution Theory, Locally Convex Spaces, Basics of Probability Theory, Hausdorff Measure and Dimension. Selected topics include Bernstein Polynomials, Pointwise Converge of Fourier Series, Lp spaces, Brownian Motion, Measures on Polish Spaces, Haar Measure, Convexity, Alexandroff–Hau...(展开全部)

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the...(展开全部)

"A Course in Real Analysis" provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progr...(展开全部)

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis...Many interesting and important applications are included...It includes an abundance of exercises, and is written in the...(展开全部)

This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional analysis...Many interesting and important applications are included...It includes an abundance of exercises, and is written in the...(展开全部)

This book is a primer in harmonic analysis on the undergraduate level. It gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. In contrast to other books on the topic, A First Course in Harmonic Analysis is entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topolo...(展开全部)

Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory. "A Course in Abstract Harmonic Analysis" offers a concise, read...(展开全部)

"Real Analysis" is the third volume in the "Princeton Lectures in Analysis", a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the serie...(展开全部)