Measures, Integrals and Martingales
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- Author: René L. Schilling, Technische Universität, Dresden
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This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached at http://www.motapa.de/measures_integrals_and_martingales/index.htmlRead more
- Introduction to a central mathematical topic accessible for undergraduates
- Easy to follow exposition with numerous illustrations and exercises included; hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259
- Text is suitable for classroom use as well as for self-study
Reviews & endorsements
"I believe this to be a great book for self-study as well as for course use. The book is ideal for future probabilists as well as statisticians, and can serve as a good introduction for mathematicians interested in measure theory."
MAA ReviewsSee more reviews
"...it succeeds in handling the technicalities of measure theory, which is traditionally regarded as dry and inaccessible to students (and, I think, the most difficult material that I have taught at undergraduate level) with a light touch. The book is eminently suitable for a course (or two) for good final year or first-year post-graduate students and has the potential to revitalize the way that measure theory is taught. If it does, the author will deserve our thanks indeed."
Journal of the Royal Statistical Society
"This book will remain a good reference on the subject for years to come."
Peter Eichelsbacher, Mathematical Reviews
"The chapters contain nicely written short blocks of theory followed by good and meaningful exercises, solutions of which are available on the author's home page. This feature makes the book an attractive starting point for an undergraduate course on measure and integration theory. The book is well structured and the presentation is clear; arguments and proofs are detailed and easy to follow."
Filip Lindskog, Journal of the American Statistical Association
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- Date Published: December 2007
- format: Adobe eBook Reader
- isbn: 9780511343339
- contains: 15 b/w illus. 500 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. The pleasures of counting
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
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
Name and subject index.
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