Real Analysis and Functional Analysis

Author: Guo Maozheng
Publisher:
Publish Date: 2005-02-01
Features: This textbook is designed for university non-foundational mathematics majors taking the course "Real Analysis and Functional Analysis." Its prerequisites are Mathematical Analysis or Advanced Mathematics for physics majors. The book is divided into 6 chapters, covering the following topics: Sets, Euclidean Spaces, Lebesgue Measure, Lebesgue Measurable Functions, Lebesgue Integration, Measure Spaces, Measurable Functions and Integrals on Measure Spaces, Lp Spaces, L2 Spaces, Convolution and Fourier Transform, Hilbert Space Theory, Bounded Linear Operators on Hilbert Spaces, Banach Spaces, Bounded Linear Operators on Banach Spaces, Continuous Linear Functionals on Banach Spaces, Conjugate Spaces and Conjugate Operators, Convergence and Compactness in Banach Spaces. The book emphasizes a concise and focused approach to the selection of materials, highlighting key concepts and fully reflecting the core content of Real Analysis and Functional Analysis. The content is presented in a progressive and systematic manner, with new theories introduced alongside their background and connections to previous concepts. The writing is rigorous, concise, clear, and easy to read, making it suitable for both teaching and self-study. To aid readers in reviewing, consolidating, understanding, and expanding their knowledge, each section is followed by a rich set of exercises. To ensure the book is self-contained, four appendices have been specially compiled to provide rigorous mathematical proofs for all theorems in the text. At the end of the book, reference solutions or hints are provided for some exercises. This book can serve as a textbook or teaching reference for undergraduate students in disciplines such as applied mathematics, computational mathematics, statistics, physics, and related fields, as well as for researchers in mathematics or physics. The book is divided into 6 chapters, covering topics such as Sets, Euclidean Spaces, Lebesgue Measure, Lebesgue Measurable Functions, Lebesgue Integration, Measure Spaces, Measurable Functions and Integrals on Measure Spaces, etc.