Counterexamples in measure and integration

著者

書誌事項

Counterexamples in measure and integration

René L. Schilling, Franziska Kühn

Cambridge University Press, 2021

  • [: pbk.]

大学図書館所蔵 件 / 全4件

この図書・雑誌をさがす

注記

Includes bibliographical references (p. [385]-393) and index

内容説明・目次

内容説明

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).

目次

  • Preface
  • 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-Nikodym and related results
  • 18. Function spaces
  • 19. Convergence of measures
  • References
  • Index.

「Nielsen BookData」 より

詳細情報

ページトップへ