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  • © 1965

Real and Abstract Analysis

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

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  • ISBN: 978-3-642-88044-5
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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VIII
  2. Set Theory and Algebra

    • Edwin Hewitt, Karl Stromberg
    Pages 1-52
  3. Topology and Continuous Functions

    • Edwin Hewitt, Karl Stromberg
    Pages 53-103
  4. The Lebesgue Integral

    • Edwin Hewitt, Karl Stromberg
    Pages 104-187
  5. Function Spaces and Banach Spaces

    • Edwin Hewitt, Karl Stromberg
    Pages 188-255
  6. Differentiation

    • Edwin Hewitt, Karl Stromberg
    Pages 256-376
  7. Integration on Product Spaces

    • Edwin Hewitt, Karl Stromberg
    Pages 377-459
  8. Back Matter

    Pages 460-476

About this book

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

  • The University of Washington, USA

    Edwin Hewitt

  • The University of Oregon, USA

    Karl Stromberg

Bibliographic Information

  • Book Title: Real and Abstract Analysis

  • Book Subtitle: A modern treatment of the theory of functions of a real variable

  • Authors: Edwin Hewitt, Karl Stromberg

  • DOI: https://doi.org/10.1007/978-3-642-88044-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1965

  • Softcover ISBN: 978-3-642-88046-9

  • eBook ISBN: 978-3-642-88044-5

  • Edition Number: 1

  • Number of Pages: VIII, 476

  • Topics: Real Functions, Analysis

Buying options

eBook
USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-88044-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 89.99
Price excludes VAT (USA)