© 2013

Measure Theory

Second Edition


Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Donald L. Cohn
    Pages 1-40
  3. Donald L. Cohn
    Pages 41-77
  4. Donald L. Cohn
    Pages 79-111
  5. Donald L. Cohn
    Pages 113-141
  6. Donald L. Cohn
    Pages 143-154
  7. Donald L. Cohn
    Pages 155-179
  8. Donald L. Cohn
    Pages 181-237
  9. Donald L. Cohn
    Pages 239-277
  10. Donald L. Cohn
    Pages 279-306
  11. Donald L. Cohn
    Pages 307-371
  12. Back Matter
    Pages 373-457

About this book


Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings.

Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.


The author aims to present  a straightforward treatment of the part of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topology...Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to important extensions and developments of the theory; for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation of materials makes this a useful book for an introduction to measure and integration theory.

—Mathematical Reviews (Review of the First Edition)


The book is a comprehensive and clearly written textbook on measure and integration...The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a number of exercises.  

—zbMATH (Review of the First Edition)


Banach-Tarski paradox Borel subsets Daniell integral Kurzweil-Henstock integral measure-theoretic probability theory

Authors and affiliations

  1. 1.Suffolk University Dept. Mathematics & Computer ScienceBostonUSA

Bibliographic information


From the book reviews:

“This textbook provides a comprehensive and consistent introduction to measure and integration theory. … The book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.” (Ville Suomala, Mathematical Reviews, July, 2014)

“In this second edition, Cohn has updated his excellent introduction to measure theory … and has made this great textbook even better. Those readers unfamiliar with Cohn’s style will discover that his writing is lucid. … this is a wonderful text to learn measure theory from and I strongly recommend it.” (Tushar Das, MAA Reviews, June, 2014)