Real Analysis

Author: Zhou Minqiang
Publisher:
Publish Date: 2004-03-01
Features: This book is a key textbook for the "Nine-Five" period of general higher education, specifically designed for undergraduate students in mathematics departments of comprehensive universities, science and engineering universities, and normal universities. It serves as a course textbook for "Real Analysis," primarily introducing the theory of Lebesgue measure and integration. The book is divided into six chapters: Sets and Point Sets, Lebesgue Measure, Measurable Functions, Lebesgue Integration, Differentiation and Indefinite Integration, and Lp Spaces. The author has been teaching "Real Analysis" at Peking University for 30 years, possessing extensive teaching experience and a deep understanding of students' difficulties and confusions. Therefore, the selection of content and background material in this book has been carefully arranged by the author after thorough consideration, reflecting a summary of teaching practices. The book includes abundant examples to demonstrate the broad application scope for readers. Each chapter concludes with selected thought-provoking questions and numerous exercises, providing readers with an appropriate foundation for self-training. The notes at the end of each chapter expand or deepen the content discussed in the main text, which may be beneficial for readers aspiring to further study real analysis. For those interested in the historical development of modern integration theory, the introductory "Review of Integration Theory" and the appendix "Biography of Lebesgue" are also available for reference. To facilitate learning, the back of the book provides solutions to selected thought-provoking questions, in-class exercises, and extra-curricular selected problems, serving as a reference for both teachers and students. This book can be used as a textbook or teaching reference for "Real Analysis" courses in comprehensive universities, science and engineering universities, and normal universities, as well as for young mathematics teachers and researchers.