Introduction to Real Analysis

This textbook is a classic that has been used successfully by instructors and students for nearly three decades. It offers a timely new edition with minimal yet notable changes, retaining all the elements, presentation, and accessible exposition of previous editions. The text is understandable to the typical student enrolled in the course, while also challenging the more talented student through exercises. It includes standard topics as well as topics that are not always included in comparable texts, such as a section on the Riemann-Stieltjes integral and a proof of Lebesgues theorem. The exercises at the end of each section reinforce the concepts, and notes provide historical comments or discuss additional topics.

Format: Hardback
Length: 565 pages
Publication date: 16 March 2021
Publisher: Taylor & Francis Ltd

This renowned textbook has been an invaluable resource for instructors and students for nearly three decades. In this timely new edition, we have made minimal yet significant changes while preserving all the elements, presentation, and accessible exposition that have made previous editions so popular. To provide you with an overview of the updates, we have included a comprehensive list in the Preface of this edition.

This text is a culmination of the authors extensive experience in teaching graduate courses and the essential requirements for successful graduate study. It has been designed to be understandable to the typical student enrolled in the course, considering the diverse range of abilities, backgrounds, and motivations. Chapters one through six have been crafted to be accessible to the average student, while simultaneously offering challenges to the more talented individuals through comprehensive exercises.

Chapters seven through ten assume that the students have acquired a solid foundation in the subject matter. These chapters delve deeper into the theorems, examples, and exercises, requiring a greater level of sophistication and mathematical maturity for a thorough understanding. In addition to the standard topics covered in comparable texts, this textbook also includes unique and valuable topics.

Chapter 6 presents a comprehensive section on the Riemann-Stieltjes integral, along with a proof of Lebesgues theorem, which establishes necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and provides a brief introduction to normed linear spaces. Chapter 8 showcases a proof of the Weierstrass approximation theorem using the method of approximate identities. The inclusion of Fourier series in the text offers students an opportunity to gain exposure to this important subject.

The final chapter is a comprehensive treatment of Lebesgue measure and the Lebesgue integral, utilizing both inner and outer integrals. This chapter provides a solid foundation for those seeking to delve deeper into the realm of measure theory and integration.

In conclusion, this revised and updated edition of the textbook remains a valuable tool for instructors and students alike. Its concise yet comprehensive nature, coupled with its accessible presentation, makes it an ideal resource for advancing knowledge and understanding in the field of mathematics. Whether you are a novice or an experienced student, this textbook will undoubtedly assist you in achieving your academic goals.

Weight: 1002g
Dimension: 161 x 241 x 40 (mm)
ISBN-13: 9780367486884
Edition number: 3 New edition