Skip to content
Register Sign in Wishlist
Look Inside A Radical Approach to Lebesgue's Theory of Integration

A Radical Approach to Lebesgue's Theory of Integration

Part of Mathematical Association of America Textbooks

  • Date Published: February 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521711838


Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • Meant for advanced undergraduate and graduate students in mathematics, this lively introduction to measure theory and Lebesgue integration is rooted in and motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems and highlights some of the difficulties that were encountered as these ideas were refined. The story begins with Riemann's definition of the integral, a definition created so that he could understand how broadly one could define a function and yet have it be integrable. The reader then follows the efforts of many mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work in the late 19th and early 20th centuries of Jordan, Borel, and Lebesgue, who finally broke with Riemann's definition. Ushering in a new way of understanding integration, they opened the door to fresh and productive approaches to many of the previously intractable problems of analysis.

    • Exercises at the end of each section, allowing students to explore their understanding
    • Hints to help students get started on challenging problems
    • Boxed definitions make it easier to identify key definitions
    Read more

    Reviews & endorsements

    'This introduction to measure theory and Lebesgue integration is intended for advancerd undergraduate and graduate students in mathematics, and is rooted in and motivated by the historical questions that led to its development.' The Times Higher Education Supplement

    'Bressoud is an insightful writer and he presents this material in an enchanting fashion. The writing is scholarly but inviting, rigourous but readable.' The UMAP Journal

    'The way that facts are presented makes the book accessible for graduate or advanced undergraduate students as an alternative to the standard approach of teaching real analysis. The book will be interesting for teachers as well.' EMS Newsletter

    'I find it difficult to think of a better introduction to this cornerstone of modern mathematics and highly recommend the book to a very broad readership of students and researchers alike.' Journal of the American Statistical Association

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: February 2008
    • format: Paperback
    • isbn: 9780521711838
    • length: 344 pages
    • dimensions: 252 x 177 x 18 mm
    • weight: 0.6kg
    • contains: 120 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    2. The Riemann integral
    3. Explorations of R
    4. Nowhere dense sets and the problem with the fundamental theorem of calculus
    5. The development of measure theory
    6. The Lebesgue integral
    7. The fundamental theorem of calculus
    8. Fourier series
    9. Epilogue: A. Other directions
    B. Hints to selected exercises.

  • Instructors have used or reviewed this title for the following courses

    • Mathematics of Networks
    • Real Analysis ll
    • Real Variables I and Real Variables ll
    • Topics in Mathematics: Analysis
  • Author

    David M. Bressoud, Macalester College, Minnesota

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.