Real Analysis Textbook for General Higher Education under the "Ninety-Five" Key Program of the Ministry of Education

Author: Zhou Minqiang
Publisher:
Publishing Date: 2001-07-01
Features: This book is a key textbook for the "Nine-Five" period of the Ministry of Education's focus on general higher education, designed as a course textbook for undergraduate students in mathematics departments and applied mathematics departments of comprehensive universities, universities of science and engineering, and advanced normal universities. It primarily introduces the theory of Lebesgue measure and integration, 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 the "Real Analysis" course at Peking University for 30 years, with extensive teaching experience and a deep understanding of students' difficulties and confusions. Therefore, the selection of content in terms of difficulty and the background materials are carefully arranged by the author after thorough consideration, representing a summary of teaching practice experience. The book includes abundant examples, demonstrating broad application spaces for readers. Each chapter features selected thought questions and numerous exercises, which are categorized into Group 1 and Group 2 based on difficulty and teaching requirements, providing readers with an appropriate base for self-training. The notes at the end of each chapter expand or deepen the content of the main text, which may be beneficial for readers aspiring to further study 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 appendix "Biography of Lebesgue." To facilitate learning, the appendix at the end of the book provides solutions to some thought questions, in-class exercises, and selected out-of-class exercises for reference by teachers and students. This book can serve as a textbook or teaching reference for "Real Analysis" courses for undergraduate students in mathematics departments and applied mathematics departments of comprehensive universities, universities of science and engineering, and advanced normal universities. It is also an excellent learning reference for young mathematics teachers and mathematicians.