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Measure Theory

  • Textbook
  • © 1994

Overview

Authors:
  1. J. L. Doob

    1. Urbana, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 143)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xii
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  2. Conventions and Notation

    • J. L. Doob
    Pages 1-5

  3. Operations on Sets

    • J. L. Doob
    Pages 7-10

  4. Classes of Subsets of a Space

    • J. L. Doob
    Pages 11-16

  5. Set Functions

    • J. L. Doob
    Pages 17-36

  6. Measure Spaces

    • J. L. Doob
    Pages 37-52

  7. Measurable Functions

    • J. L. Doob
    Pages 53-72

  8. Integration

    • J. L. Doob
    Pages 73-101

  9. Hilbert Space

    • J. L. Doob
    Pages 103-121

  10. Convergence of Measure Sequences

    • J. L. Doob
    Pages 123-143

  11. Signed Measures

    • J. L. Doob
    Pages 145-156

  12. Measures and Functions of Bounded Variation on R

    • J. L. Doob
    Pages 157-177

  13. Conditional Expectation; Martingale Theory

    • J. L. Doob
    Pages 179-204

  14. Back Matter

    Pages 205-212
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Keywords

About this book

This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.

Authors and Affiliations

  • Urbana, USA

    J. L. Doob

Bibliographic Information

  • Book Title: Measure Theory

  • Authors: J. L. Doob

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0877-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94055-7Published: 17 December 1993

  • Softcover ISBN: 978-1-4612-6931-1Published: 02 October 2012

  • eBook ISBN: 978-1-4612-0877-8Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 212

  • Topics: Real Functions

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