Measures, Integrals and Martingales
With 500 exercises
(Sprache: Englisch)
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability. Undergraduate calculus and an introductory course on rigorous analysis are the only essential...
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Produktinformationen zu „Measures, Integrals and Martingales “
Klappentext zu „Measures, Integrals and Martingales “
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study.Inhaltsverzeichnis zu „Measures, Integrals and Martingales “
Prelude; Dependence chart; Prologue; 1. The pleasures of counting; 2. sigma-algebras; 3. Measures; 4. Uniqueness of measures; 5. Existance of measures; 6. Measurable mappings; 7. Measurable functions; 8. Integration of positive functions; 9. Integrals of measurable functions and null sets; 10. Convergence theroems and their applications; 11. The function spaces; 12. Product measures and Fubini's theorem; 13. Integrals with respect to image measures; 14. Integrals of images and Jacobi's transformation rule; 15. Uniform integrability and Vitali's convergence theorem; 16. Martingales; 17. Martingale convergence theorems; 18. The Radon-Nikodym theorem and other applications of martingales; 19. Inner product spaces; 20. Hilbert space; 21. Conditional expectations in L2; 22. Conditional expectations in Lp; 23. Orthonormal systems and their convergence behaviour; Appendix A. Lim inf and lim supp; Appendix B. Some facts from point-set topology; Appendix C. The volume of a parallelepiped; Appendix D. Non-measurable sets; Appendix E. A summary of the Riemann integral; Further reading; Bibliography; Notation index; Name and subject index.
Autoren-Porträt von Rene Schilling
Rene Schilling is a Professor of Stochastics at the University of Marburg.
Bibliographische Angaben
- Autor: Rene Schilling
- 2005, 394 Seiten, 35 Abbildungen, Maße: 17,1 x 24,4 cm, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521615259
- ISBN-13: 9780521615259
- Erscheinungsdatum: 10.11.2005
Sprache:
Englisch
Rezension zu „Measures, Integrals and Martingales “
'... thorough introduction to a wide variety of first year graduate level topics in analysis... accessible to anyone with a strong undergraduate background in calculus, linear algebra, and real analysis.' Zentralblatt MATH 'This is a concise and elementary introduction to measure and integration theory as need nowadays in many parts of analysis and probability theory.' L'Enseignement Mathematique 'I have not seen some of the topics that are mentioned above ... treated successfully at undergraduate level before, and the book is worth having for these alone ... [it] has the potential to revitalize the way that measure theory is taught.' Journal of the Royal Statistical Society
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