《概率和鞅》的最大特点是将概率论讲述的清新易懂，通过有选择性的讲述,恰到好处的给出了理解基础部分的关键,一些测度论的重要观点都在《概率和鞅》的主体部分给出了很好的表述。附录中给出了有关测度论的完整证明。 |
| preface-please read! a question of terminology a guide to notation chapter 0 a branching-process example papr a: foundations chapter 1 measure spaces chapter 2 events chapter 3 random variables chapter 4 independence chapter 5 integration chapter 6 expectation chapter 7 an easy strong law chapter 8 product measure part b: martingale theory chapter 9 conditional expectation chapter 10 martingales chapter 11 the convergence theorem chapter 12 martingales bounded in chapter 13 uniform integrability chapter 14 ui martingales . chapter 15 applications part c characteristic functions chapter 16 basic properties of cfs chapter 17 weak convergence chapter 18 the central limit theorem appendices chapter a1：appendix to chapter 1 chapter a3：appendix to chapter 3 chapter a4：appendix to chapter 4 chapter a5：appendix to chapter 5 chapter a9：appendix to chapter 9 chapter a13：appendix to chapter 13 chapter a14：appendix to chapter 14 chapter a18：appendix to chapter 16 chapter e: exercises references index |
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