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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.
List of contents
Prologue.- Measures.- Integrations.- Signed Measures and Differentiation.- Topology: A Generalization of Open Sets.- Elements of Functional Analysis.- Lp Spaces.
About the author
Xiaochang Wang is a professor in the Department of Mathematics at Texas Tech University.
Summary
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.
Additional text
“The presentation of the chosen material is precise and intuitive. … This concise textbook may be useful for students in their self-learning, and for teachers who prepare systematic lectures on real analysis.” (Marek Balcerzak, Mathematical Reviews, July, 2019)
“The resulting book, that also features several examples and exercise problems to illustrate key concepts, is very clear and pleasant to read. In my opinion, the author fully successes in, using his own words, ‘helping students to see that the Lebesgue measure and integration, and therefore the general measure theory, come naturally from the process of fixing the flaws of Riemann integrals’.” (Emma D’Aniello, zbMATH 1423.26003, 2019)
Report
"The presentation of the chosen material is precise and intuitive. ... This concise textbook may be useful for students in their self-learning, and for teachers who prepare systematic lectures on real analysis." (Marek Balcerzak, Mathematical Reviews, July, 2019)
"The resulting book, that also features several examples and exercise problems to illustrate key concepts, is very clear and pleasant to read. In my opinion, the author fully successes in, using his own words, 'helping students to see that the Lebesgue measure and integration, and therefore the general measure theory, come naturally from the process of fixing the flaws of Riemann integrals'." (Emma D'Aniello, zbMATH 1423.26003, 2019)
