Book contents
- Frontmatter
- Contents
- Preface to the Cambridge Edition
- 1 Foundations; Set Theory
- 2 General Topology
- 3 Measures
- 4 Integration
- 5 Lp Spaces; Introduction to Functional Analysis
- 6 Convex Sets and Duality of Normed Spaces
- 7 Measure, Topology, and Differentiation
- 8 Introduction to Probability Theory
- 9 Convergence of Laws and Central Limit Theorems
- 10 Conditional Expectations and Martingales
- 11 Convergence of Laws on Separable Metric Spaces
- 12 Stochastic Processes
- 13 Measurability: Borel Isomorphism and Analytic Sets
- Appendix A Axiomatic Set Theory
- Appendix B Complex Numbers, Vector Spaces, and Taylor's Theorem with Remainder
- Appendix C The Problem of Measure
- Appendix D Rearranging Sums of Nonnegative Terms
- Appendix E Pathologies of Compact Nonmetric Spaces
- Author Index
- Subject Index
- Notation Index
- References
10 - Conditional Expectations and Martingales
Published online by Cambridge University Press: 06 July 2010
Book contents
- Frontmatter
- Contents
- Preface to the Cambridge Edition
- 1 Foundations; Set Theory
- 2 General Topology
- 3 Measures
- 4 Integration
- 5 Lp Spaces; Introduction to Functional Analysis
- 6 Convex Sets and Duality of Normed Spaces
- 7 Measure, Topology, and Differentiation
- 8 Introduction to Probability Theory
- 9 Convergence of Laws and Central Limit Theorems
- 10 Conditional Expectations and Martingales
- 11 Convergence of Laws on Separable Metric Spaces
- 12 Stochastic Processes
- 13 Measurability: Borel Isomorphism and Analytic Sets
- Appendix A Axiomatic Set Theory
- Appendix B Complex Numbers, Vector Spaces, and Taylor's Theorem with Remainder
- Appendix C The Problem of Measure
- Appendix D Rearranging Sums of Nonnegative Terms
- Appendix E Pathologies of Compact Nonmetric Spaces
- Author Index
- Subject Index
- Notation Index
- References
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- Real Analysis and Probability , pp. 336 - 384Publisher: Cambridge University PressPrint publication year: 2002
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