Real Analysis and Functional Analysis: A Summary (Third Edition), Volume 1

Author: Zhen Wei Xing
Publisher:
Publish Date: 2005-04-25
Features: This third edition maintains the features of selected content, broad applicability, and ease of teaching. It incorporates valuable feedback from many college teachers who have used the book, references the current teaching syllabus, and considers the needs of current teaching development. During revision, attention was paid to making some arguments more detailed and simplifying certain proofs. Each chapter is equipped with a summary; mathematical terminology is standardized according to current standards; examples are added, exercises are adjusted, and some recent examination questions for postgraduate entrance exams are included. Additionally, various errors in the book have been corrected. The length of the book has slightly increased.
The book consists of ten chapters: Part I includes five chapters on sets and point sets, Lebesgue measure, measurable functions, Lebesgue integration, and function spaces Lp. Part II includes five chapters on metric spaces, normed linear spaces and inner product spaces, bounded linear operators on normed spaces, bounded linear operators on inner product spaces, and an outline of generalized functions. Each chapter is followed by exercises.
This book can serve as a textbook for mathematics and applied mathematics, computational mathematics, statistical mathematics, and other related majors in comprehensive universities, technological universities, and normal universities. It can also be used as a reference book for some postgraduate students and self-learners. The prerequisite knowledge required is the basic content of mathematical analysis, linear algebra (, Volume 1 and Volume 2), ordinary differential equations, and complex analysis (Volume 2).