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Counterexamples in Measure and Integration by Franziska Kühn and René L. Schilling (2021, Hardcover)

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About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101316519139

ISBN-139781316519134

eBay Product ID (ePID)15050393018

Product Key Features

Number of Pages330 Pages

Publication NameCounterexamples in Measure and Integration

LanguageEnglish

SubjectGeneral, Mathematical Analysis

Publication Year2021

TypeTextbook

Subject AreaMathematics

AuthorFranziska Kühn, René L. Schilling

FormatHardcover

Dimensions

Item Height1.1 in

Item Weight30.7 Oz

Item Length9.9 in

Item Width6.9 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2021-017090

Reviews'... 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

Dewey Edition23

IllustratedYes

Dewey Decimal515.42

Table Of ContentPreface; User's guide; 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; References; Index.

SynopsisOften 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)., This is a perfect companion to any course on measure theory, integration, real and functional analysis, providing more than 300 examples and counterexamples to the otherwise often rather theoretical courses. By knowing 'what may go wrong' students will gain a better understanding of the standard course material.

LC Classification NumberQA312