Counterexamples in Measure and Integration
eBook - PDF

Counterexamples in Measure and Integration

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Counterexamples in Measure and Integration

Book details
Table of contents
Citations

About This Book

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).

Frequently asked questions

Simply head over to the account section in settings and click on “Cancel Subscription” - it’s as simple as that. After you cancel, your membership will stay active for the remainder of the time you’ve paid for. Learn more here.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Both plans give you full access to the library and all of Perlego’s features. The only differences are the price and subscription period: With the annual plan you’ll save around 30% compared to 12 months on the monthly plan.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes, you can access Counterexamples in Measure and Integration by René L. Schilling,Franziska Kühn in PDF and/or ePUB format, as well as other popular books in Matemáticas & Análisis matemático. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2021
ISBN
9781009020398
Topic
Matemáticas
Subtopic
Análisis matemático

Table of contents

  1. Cover
  2. Half-title Page
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Preface
  7. User’s Guide
  8. List of Topics and Phenomena
  9. 1 A Panorama of Lebesgue Integration
  10. 2 A Refresher of Topology and Ordinal Numbers
  11. 3 Riemann Is Not Enough
  12. 4 Families of Sets
  13. 5 Set Functions and Measures
  14. 6 Range and Support of a Measure
  15. 7 Measurable and Non-Measurable Sets
  16. 8 Measurable Maps and Functions
  17. 9 Inner and Outer Measure
  18. 10 Integrable Functions
  19. 11 Modes of Convergence
  20. 12 Convergence Theorems
  21. 13 Continuity and a.e. Continuity
  22. 14 Integration and Differentiation
  23. 15 Measurability on Product Spaces
  24. 16 Product Measures
  25. 17 Radon–Nikodm and Related Results
  26. 18 Function Spaces
  27. 19 Convergence of Measures
  28. References
  29. Index