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Fundamentals of Real Analysis

  • Sterling K. Berberian

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

  • Sterling K. Berberian
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

Bibliographic information

  • 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
  • Print ISBN 978-0-387-98480-3
  • Online ISBN 978-1-4612-0549-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site