Real analysis

Author: Zhou Minqiang
Publisher:
Publish Date: 2001-07-01
Features: This book is a key textbook for the "Nine-Five" national higher education project, designed for undergraduate students in mathematics departments and applied mathematics departments of comprehensive universities, universities of science and engineering, and 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 "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 materials, has been carefully arranged by the author after thorough consideration, reflecting a summary of teaching practices. The book includes numerous examples to demonstrate its broad application scope. Each chapter features selected discussion questions and a large number of exercises, which are categorized into Group 1 and Group 2 based on difficulty level and teaching requirements, providing readers with an appropriate platform for self-training. The notes at the end of each chapter expand or deepen the content of the main text, which may be helpful 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's "Biography of Lebesgue" are also available. To facilitate learning, the appendix provides solutions to selected discussion questions, in-class exercises, and extra-curricular selected problems for reference by both teachers and students. This book can serve as a textbook or teaching reference for "Real Analysis" courses in comprehensive universities, universities of science and engineering, and normal universities' mathematics and applied mathematics departments. It is also an excellent learning reference for young mathematics teachers and mathematicians.