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Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

  • Edwin Hewitt
  • Karl Stromberg

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Edwin Hewitt, Karl Stromberg
    Pages 1-52
  3. Edwin Hewitt, Karl Stromberg
    Pages 53-103
  4. Edwin Hewitt, Karl Stromberg
    Pages 104-187
  5. Edwin Hewitt, Karl Stromberg
    Pages 188-255
  6. Edwin Hewitt, Karl Stromberg
    Pages 256-376
  7. Edwin Hewitt, Karl Stromberg
    Pages 377-459
  8. Back Matter
    Pages 460-476

About this book

Introduction

This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus­ tomarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we have given elementary avatars of all important theorems, with appro­ priate suggestions for skipping. We have given complete definitions, ex­ planations, and proofs throughout, so that the book should be usable for individual study as well as for a course text. Prerequisites for reading the book are the following. The reader is assumed to know elementary analysis as the subject is set forth, for example, in TOM M. ApOSTOL'S Mathematical Analysis [Addison-Wesley Publ. Co., Reading, Mass., 1957], or WALTER RUDIN'S Principles of M athe­ nd matical Analysis [2 Ed., McGraw-Hill Book Co., New York, 1964].

Keywords

calculus function measure proof theorem variable

Authors and affiliations

  • Edwin Hewitt
    • 1
  • Karl Stromberg
    • 2
  1. 1.The University of WashingtonUSA
  2. 2.The University of OregonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-88044-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1965
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88046-9
  • Online ISBN 978-3-642-88044-5
  • Buy this book on publisher's site
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