Looking for an examination copy?
If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact firstname.lastname@example.org providing details of the course you are teaching.
Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).Read more
- More than 300 examples and counterexamples illustrating the (im)possibilities of measure and integration theory
- Concise non-technical overview of the main points of measure and integration
- Companion volume to the popular textbook Measures, Integrals and Martingales, now in its second edition
Reviews & endorsements
'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (Cambridge, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' N. H. Bingham, Imperial CollegeSee more reviews
‘… an excellent reference text and companion reader for anyone interested in deepening their understanding of measure theory.’ John Ross, MAA Reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: August 2021
- format: Paperback
- isbn: 9781009001625
- length: 420 pages
- dimensions: 244 x 170 x 23 mm
- weight: 0.74kg
- availability: In stock
Table of Contents
List of topics and phenomena
1. A panorama of Lebesgue integration
2. A refresher of topology and ordinal numbers
3. Riemann is not enough
4. Families of sets
5. Set functions and measures
6. Range and support of a measure
7. Measurable and non-measurable sets
8. Measurable maps and functions
9. Inner and outer measure
10. Integrable functions
11. Modes of convergence
12. Convergence theorems
13. Continuity and a.e. continuity
14. Integration and differentiation
15. Measurability on product spaces
16. Product measures
17. Radon–Nikodým and related results
18. Function spaces
19. Convergence of measures
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact email@example.com.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
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.×