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© 1999

Fundamentals of Real Analysis

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Sterling K. Berberian
    Pages 1-85
  3. Sterling K. Berberian
    Pages 86-114
  4. Sterling K. Berberian
    Pages 115-147
  5. Sterling K. Berberian
    Pages 148-198
  6. Sterling K. Berberian
    Pages 199-272
  7. Sterling K. Berberian
    Pages 273-363
  8. Sterling K. Berberian
    Pages 364-397
  9. Sterling K. Berberian
    Pages 398-421
  10. Sterling K. Berberian
    Pages 422-468
  11. Back Matter
    Pages 469-479

About this book

Introduction

Integration theory and general topology form the core of this textbook for a first-year graduate course in real analysis. After the foundational material in the first chapter (construction of the reals, cardinal and ordinal numbers, Zorn's lemma and transfinite induction), measure, integral and topology are introduced and developed as recurrent themes of increasing depth. The treatment of integration theory is quite complete (including the convergence theorems, product measure, absolute continuity, the Radon-Nikodym theorem, and Lebesgue's theory of differentiation and primitive functions), while topology, predominantly metric, plays a supporting role. In the later chapters, integral and topology coalesce in topics such as function spaces, the Riesz representation theorem, existence theorems for an ordinary differential equation, and integral operators with continuous kernel function. In particular, the material on function spaces lays a firm foundation for the study of functional analysis.

Keywords

convolution functional analysis integral transform real analysis matematics

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

Bibliographic information

  • Book Title Fundamentals of Real Analysis
  • Authors Sterling K. Berberian
  • Series Title Universitext
  • DOI https://doi.org/10.1007/978-1-4612-0549-4
  • Copyright Information Springer Science+Business Media New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-0-387-98480-3
  • eBook ISBN 978-1-4612-0549-4
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XI, 479
  • Number of Illustrations 98 b/w illustrations, 0 illustrations in colour
  • Topics Real Functions
  • Buy this book on publisher's site

Reviews

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS