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Measure and Category

A Survey of the Analogies between Topological and Measure Spaces

  • Textbook
  • © 1980

Overview

Authors:
  1. John C. Oxtoby

    1. Department of Mathematics, Bryn Mawr College, Bryn Mawr, USA

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

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Measure and Category on the Line

    • John C. Oxtoby
    Pages 1-5

  3. Liouville Numbers

    • John C. Oxtoby
    Pages 6-9

  4. Lebesgue Measure in r-Space

    • John C. Oxtoby
    Pages 10-18

  5. The Property of Baire

    • John C. Oxtoby
    Pages 19-21

  6. Non-Measurable Sets

    • John C. Oxtoby
    Pages 22-26

  7. The Banach-Mazur Game

    • John C. Oxtoby
    Pages 27-30

  8. Functions of First Class

    • John C. Oxtoby
    Pages 31-35

  9. The Theorems of Lusin and Egoroff

    • John C. Oxtoby
    Pages 36-38

  10. Metric and Topological Spaces

    • John C. Oxtoby
    Pages 39-41

  11. Examples of Metric Spaces

    • John C. Oxtoby
    Pages 42-44

  12. Nowhere Differentiable Functions

    • John C. Oxtoby
    Pages 45-46

  13. The Theorem of Alexandroff

    • John C. Oxtoby
    Pages 47-48

  14. Transforming Linear Sets into Nullsets

    • John C. Oxtoby
    Pages 49-51

  15. Fubini’s Theorem

    • John C. Oxtoby
    Pages 52-55

  16. The Kuratowski-Ulam Theorem

    • John C. Oxtoby
    Pages 56-61

  17. The Banach Category Theorem

    • John C. Oxtoby
    Pages 62-64

  18. The Poincaré Recurrence Theorem

    • John C. Oxtoby
    Pages 65-69

  19. Transitive Transformations

    • John C. Oxtoby
    Pages 70-73

  20. The Sierpinski-Erdös Duality Theorem

    • John C. Oxtoby
    Pages 74-77
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics, Bryn Mawr College, Bryn Mawr, USA

    John C. Oxtoby

Bibliographic Information

  • Book Title: Measure and Category

  • Book Subtitle: A Survey of the Analogies between Topological and Measure Spaces

  • Authors: John C. Oxtoby

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9339-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1980

  • Hardcover ISBN: 978-0-387-90508-2Published: 29 September 1980

  • Softcover ISBN: 978-1-4684-9341-2Published: 29 April 2012

  • eBook ISBN: 978-1-4684-9339-9Published: 01 December 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: X, 108

  • Topics: Real Functions, K-Theory, Topology

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