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© 1996

Measure Theory and Probability

Textbook

Part of the The Wadsworth & Brooks/Cole Mathematics Series book series (WBCMS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Malcolm Adams, Victor Guillemin
    Pages 1-52
  3. Malcolm Adams, Victor Guillemin
    Pages 53-117
  4. Malcolm Adams, Victor Guillemin
    Pages 118-177
  5. Back Matter
    Pages 178-205

About this book

Introduction

Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measure-theoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] (metric space approach), the Borel-Cantelli lemmas, straight measure theory (the Lebesgue integral). Chapter 3 expands on abstract Fourier analysis, Fourier series and the Fourier integral, which have some beautiful probabilistic applications: Polya's theorem on random walks, Kac's proof of the Szegö theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises.

"…the text is user friendly to the topics it considers and should be very accessible…Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association

Keywords

Lebesgue measure Probability theory calculus ksa measure theory proof random walk theorem

Authors and affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.Department of MathematicsMITCambridgeUSA

Bibliographic information

  • Book Title Measure Theory and Probability
  • Authors Malcolm Adams
    Victor Guillemin
  • Series Title The Wadsworth & Brooks/Cole Mathematics Series
  • DOI https://doi.org/10.1007/978-1-4612-0779-5
  • Copyright Information Birkhäuser Boston 1996
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-3884-9
  • Softcover ISBN 978-1-4612-6899-4
  • eBook ISBN 978-1-4612-0779-5
  • Edition Number 1
  • Number of Pages XVI, 206
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Measure and Integration
    Probability Theory and Stochastic Processes
  • Buy this book on publisher's site

Reviews

"…the text is user friendly to the topics it considers and should be very accessible…Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association