Real variable function

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 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 practice experience. The book includes numerous examples to demonstrate the broad application scope. Each chapter also features selected thought-provoking 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 beneficial 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 appendix "Biography of Lebesgue." To facilitate learning, the book includes solutions to selected thought-provoking questions, in-class exercises, and extra-curricular selected problems at the end for reference by both 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 normal universities, as well as for young mathematics teachers and researchers.