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Viser: Measures, Integrals and Martingales
Measures, Integrals and Martingales
René L. Schilling
(2005)
Sprog: Engelsk
Detaljer om varen
- Paperback: 396 sider
- Udgiver: Cambridge University Press (November 2005)
- ISBN: 9780521615259
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.