Measure and Category

A Survey of the Analogies between Topological and Measure Spaces

  • John C. Oxtoby

Part of the Graduate Texts in Mathematics book series (GTM, volume 2)

Table of contents

  1. Front Matter
    Pages I-X
  2. John C. Oxtoby
    Pages 1-5
  3. John C. Oxtoby
    Pages 6-9
  4. John C. Oxtoby
    Pages 10-18
  5. John C. Oxtoby
    Pages 19-21
  6. John C. Oxtoby
    Pages 22-26
  7. John C. Oxtoby
    Pages 27-30
  8. John C. Oxtoby
    Pages 31-35
  9. John C. Oxtoby
    Pages 36-38
  10. John C. Oxtoby
    Pages 39-41
  11. John C. Oxtoby
    Pages 42-44
  12. John C. Oxtoby
    Pages 45-46
  13. John C. Oxtoby
    Pages 47-48
  14. John C. Oxtoby
    Pages 49-51
  15. John C. Oxtoby
    Pages 52-55
  16. John C. Oxtoby
    Pages 56-61
  17. John C. Oxtoby
    Pages 62-64
  18. John C. Oxtoby
    Pages 65-69
  19. John C. Oxtoby
    Pages 70-73
  20. John C. Oxtoby
    Pages 74-77

About this book


In this edition, a set of Supplementary Notes and Remarks has been added at the end, grouped according to chapter. Some of these call attention to subsequent developments, others add further explanation or additional remarks. Most of the remarks are accompanied by a briefly indicated proof, which is sometimes different from the one given in the reference cited. The list of references has been expanded to include many recent contributions, but it is still not intended to be exhaustive. John C. Oxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not essential for present purposes-the Riemann integral is sufficient. Concepts of general measure theory and topology are introduced, but not just for the sake of generality. Needless to say, the term "category" refers always to Baire category; it has nothing to do with the term as it is used in homological algebra.


Kategorie (Math.) Mass (Math.) algebra automorphism homological algebra measure theory set set of first category topological space topology

Authors and affiliations

  • John C. Oxtoby
    • 1
  1. 1.Department of MathematicsBryn Mawr CollegeBryn MawrUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9341-2
  • Online ISBN 978-1-4684-9339-9
  • Series Print ISSN 0072-5285
  • About this book