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Counterexamples in Measure and Integration.
・ISBN 978-1-316-51913-4 hard GB£ 116.00
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★★★
電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-00379-7
| 著者・編者 | Schilling, Rene L. / Kuehn, Franziska, |
|---|---|
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2021 |
| ページ数 | 330 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-9582＞ |
解説
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 Rene Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).