Real Analysis

Author: Zhou Minqiang
Publisher:
Publish Date: 2003-11-14
Features: This book is a key textbook for the "Nine-Five" period of the Ministry of Education's general higher education program, designed for undergraduate students in mathematics departments of comprehensive universities, science and engineering universities, and teacher training universities. It primarily introduces the theory of Lebesgue measure and integration, covering 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 in this book, including its difficulty level and the background material, has been carefully arranged by the author after thorough consideration. It is a summary of teaching practices and includes numerous examples to demonstrate the broad application scope. Each chapter is followed by selected discussion questions and a large number of exercises, providing readers with an appropriate platform for self-training. The notes at the end of each chapter expand or deepen the content discussed in the main text, which may be helpful for readers interested in further studying real analysis. If readers are interested in the historical development of modern integration theory, they can also read the introductory "Review of Integration Theory" and the "Biography of Lebesgue" in the appendix. To facilitate learning, the solutions to selected discussion questions, in-class exercises, and extra selected problems are provided at the end of the book for reference by teachers and students. This book can serve as a textbook or teaching reference for "Real Analysis" courses in comprehensive universities, science and engineering universities, and teacher training universities for mathematics departments and applied mathematics departments. It is also an excellent learning reference for young mathematics teachers and mathematicians.