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Lecture Notes in Real Analysis

  • Textbook
  • © 2018

Overview

Authors:
  1. Xiaochang Wang

    1. Math & Stats, Texas Tech University, Lubbock, USA

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  • Presents graduate-level material in a compact, more intuitive manner
  • Combines elements from two classic Real Analysis textbooks to provide a more concise approach to the material
  • Includes several color illustrations to aid in the explanation of more difficult concepts

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Measures

    • Xiaochang Wang
    Pages 1-37

  3. Integration

    • Xiaochang Wang
    Pages 39-89

  4. Signed Measures and Differentiation

    • Xiaochang Wang
    Pages 91-121

  5. Topology: A Generalization of Open Sets

    • Xiaochang Wang
    Pages 123-146

  6. Elements of Functional Analysis

    • Xiaochang Wang
    Pages 147-174

  7. Lp Spaces

    • Xiaochang Wang
    Pages 175-204

  8. Back Matter

    Pages 205-207
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Keywords

About this book

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.   

Reviews

“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)

Authors and Affiliations

  • Math & Stats, Texas Tech University, Lubbock, USA

    Xiaochang Wang

About the author

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

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