Lebesgue Integration

  • Authors
  • Soo Bong Chae

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Soo Bong Chae
    Pages 1-23
  3. Soo Bong Chae
    Pages 24-49
  4. Soo Bong Chae
    Pages 50-86
  5. Soo Bong Chae
    Pages 87-124
  6. Soo Bong Chae
    Pages 125-154
  7. Soo Bong Chae
    Pages 191-233
  8. Back Matter
    Pages 234-264

About this book

Introduction

Responses from colleagues and students concerning the first edition indicate that the text still answers a pedagogical need which is not addressed by other texts. There are no major changes in this edition. Several proofs have been tightened, and the exposition has been modified in minor ways for improved clarity. As before, the strength of the text lies in presenting the student with the difficulties which led to the development of the theory and, whenever possi­ ble, giving the student the tools to overcome those difficulties for himself or herself. Another proverb: Give me a fish, I eat for a day. Teach me to fish, I eat for a lifetime. Soo Bong Chae March 1994 Preface to the First Edition This book was developed from lectures in a course at New College and should be accessible to advanced undergraduate and beginning graduate students. The prerequisites are an understanding of introductory calculus and the ability to comprehend "e-I) arguments. " The study of abstract measure and integration theory has been in vogue for more than two decades in American universities since the publication of Measure Theory by P. R. Halmos (1950). There are, however, very few ele­ mentary texts from which the interested reader with a calculus background can learn the underlying theory in a form that immediately lends itself to an understanding of the subject. This book is meant to be on a level between calculus and abstract integration theory for students of mathematics and physics.

Keywords

Derivative Fourier series Fundamental theorem of calculus Hilbert space Riemann integral differential equation measure

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0781-8
  • Copyright Information Springer-Verlag New York, Inc. 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94357-2
  • Online ISBN 978-1-4612-0781-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book