Counterexamples in Measure and Integration
«'Counterexamples in Measure and Integration is an ideal companion to help better understand canonically problematic examples in analysis … This collection of counterexamples is an excellent resource to researchers who rely on measure and integration theory. It would be helpful for students studying for their analysis qualifying exam as it draws on common misconceptions and enables readers to build intuition about why a given counterexample works and how conditions can be changed to make a particular statement hold.' Katelynn Kochalski, Notices of the AMS»
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. Les mer
Detaljer
- Forlag
- Cambridge University Press
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9781316519134
- Utgivelsesår
- 2021
- Format
- 25 x 17 cm
Anmeldelser
«'Counterexamples in Measure and Integration is an ideal companion to help better understand canonically problematic examples in analysis … This collection of counterexamples is an excellent resource to researchers who rely on measure and integration theory. It would be helpful for students studying for their analysis qualifying exam as it draws on common misconceptions and enables readers to build intuition about why a given counterexample works and how conditions can be changed to make a particular statement hold.' Katelynn Kochalski, Notices of the AMS»
«'The book is well written, the demonstrations are clear and the bibliographic references are competent. We appreciate this work as extremely useful for those interested in measure theory and integration, starting with beginners and extending even to advanced researchers in the field.' Liviu Constantin Florescu, Mathematical Reviews/MathSciNet»
«'… the unique nature of the book makes it an essential acquisition for any university with a doctoral program in pure mathematics … Essential.' M. Bona, Choice Connect»
«'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 College»
«'… an excellent reference text and companion reader for anyone interested in deepening their understanding of measure theory.' John Ross, MAA Reviews»