Real Analysis (Second Edition)

Author: Jiang Zejian
Publisher:
Publish Date: 2003-04-02
Features: The second edition of this book was revised based on the outline for the textbook "Real Analysis" formulated by the Editorial Committee of Function Theory and Functional Analysis of the Science and Engineering Mathematics Editorial Board in November 1990. The second edition maintains the system and features of the first edition, with substantial enrichment and improvements in content. Minor adjustments were made to the order of some chapters, and the number of exercises was appropriately increased. For some slightly more challenging problems, stage-by-stage hints were provided. The newly added sections include: "Extension of Measure on a Set Ring," "Lebesgue Integral Theory, Signed Measure, Jordan-Hahn Decomposition, Radon-Nikodym Theorem on General Measure Spaces," and "Extension from Real L2 Spaces to Complex LP Spaces (P ≥ 1)." The application of Fourier series and Fejesgue integral is also newly added, showcasing its brilliant applications. The book is written in clear and concise language with rigorous proofs, and it pays great attention to cultivating students' abilities to analyze and solve problems. The content marked with is optional for students with stronger academic backgrounds. This book can serve as a textbook for foundational mathematics, computational mathematics, and applied mathematics programs in comprehensive universities, engineering universities, and normal universities, as well as a self-study reference.