Counterexamples in Measure and Integration

Explore measure and integration theory by asking 'What can go wrong if...' with this selection of over 300 counterexamples.

List of contents

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-Nikodým and related results; 18. Function spaces; 19. Convergence of measures; References; Index.

About the author

René L. Schilling is Professor of Probability Theory at Technische Universität Dresden. His research focuses on stochastic analysis and the theory of stochastic processes.Franziska Kühn is Research Assistant at Technische Universität Dresden, where she finished her Ph.D. in 2016. She is interested in the interplay of probability theory and analysis, with a focus on jump processes and non-local operators.

Product details

• Authors: Franziska (Technische Universitat Kuhn, Franziska Kühn, René L Schilling, René L. Schilling, Rene L. (Technische Universitat Schilling
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2021
• EAN: 9781316519134
• ISBN: 978-1-316-51913-4
• No. of pages: 330
• Subjects: Natural sciences, medicine, IT, technology > Natural sciences (general); MATHEMATICS / Mathematical Analysis, Scientific standards, measurement etc, Probability & statistics, Calculus & mathematical analysis, Probability and statistics, Calculus and mathematical analysis, Mensuration & Systems Of Measurement