图书简介

List of symbols; Prelude; Dependence chart; 1. Prologue; 2. The pleasures of counting; 3. ?-algebras; 4. Measures; 5. Uniqueness of measures; 6. Existence of measures; 7. Measurable mappings; 8. Measurable functions; 9. Integration of positive functions; 10. Integrals of measurable functions; 11. Null sets and the ?almost everywhere?; 12. Convergence theorems and their applications; 13. The function spaces Lp; 14. Product measures and Fubini?s theorem; 15. Integrals with respect to image measures; 16. Jacobi?s transformation theorem; 17. Dense and determining sets; 18. Hausdorff measure; 19. The Fourier transform; 20. The Radon?Nikodym theorem; 21. Riesz representation theorems; 22. Uniform integrability and Vitali?s convergence theorem; 23. Martingales; 24. Martingale convergence theorems; 25. Martingales in action; 26. Abstract Hilbert spaces; 27. Conditional expectations; 28. Orthonormal systems and their convergence behaviour; Appendix A. Lim inf and lim sup; Appendix B. Some facts from topology; Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali?s covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index.

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