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245884728
Counterexamples in Measure and Integration
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Item #:
245884728
GHS 1140
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Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails'.
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What Stands Out
Rigorous Examples
Offers carefully constructed counterexamples that challenge standard measure theory principles, enhancing comprehension for both students and professionals in mathematics.
Clarity and Insight
Breaks down complex concepts into understandable scenarios, providing clear insight into common misconceptions in measure and integration topics. Suitable for learners at various levels.
Comprehensive Coverage
Thoroughly covers a diverse range of counterexamples, effectively illustrating nuanced situations in measure theory, thereby equipping readers with deeper analytical skills.
Product Details
- 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).
| Publisher | Cambridge University Press |
| Publication date | June 17, 2021 |
| Edition | 1st |
| Language | English |
| File size | 7.1 MB |
| Enhanced typesetting | Not Enabled |
| X-Ray | Not Enabled |
| Word Wise | Not Enabled |
| Print length | 430 pages |
| Format | Print Replica |
| ISBN-13 | 978-1009020398 |
| Page Flip | Not Enabled |
| Item Weight | 0.9 lbs (410 grams) |
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Features & Benefits
- Discover over 300 instructive counterexamples that reveal the pitfalls of measure and integration.
- Gain a deep understanding of what can go wrong in measure theory.
- Accessible to advanced undergraduates with only modest prerequisites.
- Includes relevant theory contexts and suggestions for further reading.
- Self-contained overview ensures easy comprehension for self-study or supplemental learning.
- Ideal for researchers aiming to navigate the limitations of general measure theory.
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