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Problems in Analysis

  • Bernard R. Gelbaum

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Problems

    1. Front Matter
      Pages 1-1
    2. Bernard R. Gelbaum
      Pages 3-4
    3. Bernard R. Gelbaum
      Pages 5-7
    4. Bernard R. Gelbaum
      Pages 8-9
    5. Bernard R. Gelbaum
      Pages 10-14
    6. Bernard R. Gelbaum
      Pages 15-19
    7. Bernard R. Gelbaum
      Pages 20-22
    8. Bernard R. Gelbaum
      Pages 23-27
    9. Bernard R. Gelbaum
      Pages 28-30
    10. Bernard R. Gelbaum
      Pages 31-34
    11. Bernard R. Gelbaum
      Pages 35-37
    12. Bernard R. Gelbaum
      Pages 38-42
    13. Bernard R. Gelbaum
      Pages 43-46
    14. Bernard R. Gelbaum
      Pages 47-48
    15. Bernard R. Gelbaum
      Pages 49-54
    16. Bernard R. Gelbaum
      Pages 55-64
  3. Solutions

    1. Front Matter
      Pages 65-65
    2. Bernard R. Gelbaum
      Pages 67-68
    3. Bernard R. Gelbaum
      Pages 69-75
    4. Bernard R. Gelbaum
      Pages 76-78
    5. Bernard R. Gelbaum
      Pages 79-87
    6. Bernard R. Gelbaum
      Pages 88-100
    7. Bernard R. Gelbaum
      Pages 101-108
    8. Bernard R. Gelbaum
      Pages 109-117
    9. Bernard R. Gelbaum
      Pages 118-125
    10. Bernard R. Gelbaum
      Pages 126-132
    11. Bernard R. Gelbaum
      Pages 133-138
    12. Bernard R. Gelbaum
      Pages 139-148
    13. Bernard R. Gelbaum
      Pages 149-158
    14. Bernard R. Gelbaum
      Pages 159-164
    15. Bernard R. Gelbaum
      Pages 165-177
    16. Bernard R. Gelbaum
      Pages 178-202
  4. Back Matter
    Pages 203-206

About this book

Introduction

These problems and solutions are offered to students of mathematics who have learned real analysis, measure theory, elementary topology and some theory of topological vector spaces. The current widely used texts in these subjects provide the background for the understanding of the problems and the finding of their solutions. In the bibliography the reader will find listed a number of books from which the necessary working vocabulary and techniques can be acquired. Thus it is assumed that terms such as topological space, u-ring, metric, measurable, homeomorphism, etc., and groups of symbols such as AnB, x EX, f: IR 3 X 1-+ X 2 - 1, etc., are familiar to the reader. They are used without introductory definition or explanation. Nevertheless, the index provides definitions of some terms and symbols that might prove puzzling. Most terms and symbols peculiar to the book are explained in the various introductory paragraphs titled Conventions. Occasionally definitions and symbols are introduced and explained within statements of problems or solutions. Although some solutions are complete, others are designed to be sketchy and thereby to give their readers an opportunity to exercise their skill and imagination. Numbers written in boldface inside square brackets refer to the bib­ liography. I should like to thank Professor P. R. Halmos for the opportunity to discuss with him a variety of technical, stylistic, and mathematical questions that arose in the writing of this book. Buffalo, NY B.R.G.

Keywords

Analysis /Aufgabensammlung calculus measure measure theory real analysis

Authors and affiliations

  • Bernard R. Gelbaum
    • 1
  1. 1.Department of MathematicsState University of New YorkBuffaloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7679-2
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-7681-5
  • Online ISBN 978-1-4615-7679-2
  • Series Print ISSN 0941-3502
  • Buy this book on publisher's site
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