Lecture Notes in Real Analysis

✍ Scribed by Xiaochang Wang

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 217
• Series: Compact Textbooks in Mathematics
• Category: Library

✦ Synopsis

This compact textbook is a collection of the author’s lecture notes for a two-semester graduate-level real analysis course. While the material covered is standard, the author’s approach is unique in that it combines elements from both Royden’s and Folland’s classic texts to provide a more concise and intuitive presentation. Illustrations, examples, and exercises are included that present Lebesgue integrals, measure theory, and topological spaces in an original and more accessible way, making difficult concepts easier for students to understand. This text can be used as a supplementary resource or for individual study.

✦ Table of Contents

Front Matter ....Pages i-xiii
Measures (Xiaochang Wang)....Pages 1-37
Integration (Xiaochang Wang)....Pages 39-89
Signed Measures and Differentiation (Xiaochang Wang)....Pages 91-121
Topology: A Generalization of Open Sets (Xiaochang Wang)....Pages 123-146
Elements of Functional Analysis (Xiaochang Wang)....Pages 147-174
Lp Spaces (Xiaochang Wang)....Pages 175-204
Back Matter ....Pages 205-207

✦ Subjects

Mathematical Analysis, Functional Analysis, Measure Theory