Real Analysis and Functional Analysis - (Second Edition) (Two Volumes)

Author: Guo DaJun, Huang ChunChao, Liang FangHao, Wei ZhongLi / Country: Mainland China
Publisher:
Publish Date: 2005-07-01
Features: This book is divided into fourteen chapters. Chapters 1 to 6 cover the content of real analysis (Volume 1), including sets and point sets, measure, measurable functions and Lebesgue integration, Riemann-Stieltjes integration and Lebesgue-Stieltjes integration, etc. It also introduces abstract measure and integration. Chapters 7 to 14 cover the content of functional analysis (Volume 2), including metric spaces and Banach spaces, Hilbert spaces, linear operators and linear functionals, completely continuous operators, self-adjoint operators, etc. It also introduces abstract functions and Banach algebras, convex cone theory, and generalized functions. Each chapter ends with a substantial number of exercises. The book divides the content into basic and non-basic aspects. The basic content is written in detail, with a focus on being rigorous yet accessible and easy to understand. For non-basic content, an asterisk () is added to the title, indicating optional reading. This book can serve as a textbook or reference for mathematics departments in comprehensive universities and normal universities for the courses "Real Analysis" and "Functional Analysis." It can also be used by mathematics enthusiasts for self-study in these two subjects.