TOC Front Cover 2 Probabilities and Potential 5 Copyright Page 6 Contents 7 CHAPTER 0. NOTATION 15 CHAPTER I. MEASURABLE SPACES 21 1. σ-fields and random variables 21 2. Real-valued random variables 25 CHAPTER II. PROBABILITY LAWS AND MATHEMATICAL EXPECTATIONS 31 1. Summary of integration theory 31 2. Supplement on integration 35 3. Completion, independence, conditioning 44 CHAPTER III. COMPLEMENTS TO MEASURE THEORY 53 1. Analytic sets 53 2. Capacities 65 Front Cover 2 Probabilities and Potential 5 Copyright Page 6 Contents 7 CHAPTER 0. NOTATION 15 CHAPTER I. MEASURABLE SPACES 21 1. σ-fields and random variables 21 2. Real-valued random variables 25 CHAPTER II. PROBABILITY LAWS AND MATHEMATICAL EXPECTATIONS 31 1. Summary of integration theory 31 2. Supplement on integration 35 3. Completion, independence, conditioning 44 CHAPTER III. COMPLEMENTS TO MEASURE THEORY 53 1. Analytic sets 53 2. Capacities 65 3. Bounded Radon measures 79 CHAPTER IV. STOCHASTIC PROCESSES 97 1. General properties of processes 97 2. Regularity of paths 103 3. Optional and predictable times 128 4. Examples and supplements 157 APPENDIX TO CHAPTER III 169 APPENDIX TO CHAPTER IV 177 COMMENTS 183 INDEX OF TERMINOLOGY 189 INDEX OF NOTATION 195 BIBLIOGRAPHY 199 Show more