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.

Autorentext

Xiaochang Wang is a professor in the Department of Mathematics at Texas Tech University.

Inhalt

Prologue.- Measures.- Integrations.- Signed Measures and Differentiation.- Topology: A Generalization of Open Sets.- Elements of Functional Analysis.- Lp Spaces.