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 changes while retaining all the elements, presentation, and accessible exposition of previous editions. The chapters are written to be accessible to the average student while challenging the more talented student through exercises. It also includes topics that are not always included in comparable texts, such as the Riemann-Stieltjes integral, square summable sequences, the Weierstrass approximation theorem, Fourier series, and Lebesgue measure and the Lebesgue integral. The exercises at the end of each section reinforce the concepts, and notes provide historical comments or discuss additional topics.

Format: Paperback / softback
Length: 582 pages
Publication date: 03 July 2023
Publisher: Taylor & Francis Ltd

This renowned textbook has been an invaluable resource for instructors and students for nearly three decades, delivering comprehensive and accessible coverage of its subject matter. In this timely new edition, the authors have made thoughtful yet minimal changes, ensuring that all the essential elements, presentation, and accessible exposition of previous editions remain intact. To assist readers, a comprehensive list of updates is provided in the Preface of this edition.

This text is crafted based on the authors extensive experience in teaching graduate courses and the fundamental requirements for successful graduate study. It is designed to be understandable to the typical student enrolled in the course, taking into account the diverse abilities, backgrounds, and motivations of the student body. Chapters one through six have been carefully 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 a certain level of expertise in the subject matter, presenting theorems, examples, and exercises that demand greater sophistication and mathematical maturity for a full understanding. In addition to the standard topics commonly found in comparable texts, this textbook includes unique and valuable topics that are often overlooked.

Chapter six, for instance, delves into the Riemann-Stieltjes integral, providing a comprehensive proof of Lebesgues theorem, which establishes necessary and sufficient conditions for Riemann integrability. Chapter seven also includes a section on square summable sequences, offering a brief introduction to normed linear spaces. Chapter eight showcases a proof of the Weierstrass approximation theorem using the method of approximate identities, while Chapter nine introduces Fourier series, providing students with valuable exposure to this important subject.

The final chapter of the textbook is dedicated to a detailed treatment of Lebesgue measure and the Lebesgue integral, employing both inner and outer measures. This comprehensive coverage provides students with a solid foundation in these fundamental concepts, equipping them with the tools they need to excel in their academic pursuits.

In summary, this classic textbook has been revised and updated to meet the evolving needs of instructors and students, while preserving its timeless and enduring quality. With its comprehensive content, accessible presentation, and timely updates, it remains a valuable resource for anyone seeking to delve deeper into the world of mathematics.

Weight: 860g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367683931
Edition number: 3 ed