概率与测度 word 网盘 高速 下载地址大全 免费

本书是《概率与测度》第3版，新版保留了原先的风格，将测度论和概率论有机结合在一起，把相关内容混合排列。概率问题会引起学生学习测度论的兴趣，而测度论知识又反过来应用到概率论中。本书主要内容包括概率、测度、积分、随机变量及数学期望、分布的收敛问题、导数与条件期望，随机过程等。本版改进了布朗运动的叙述方式，并以遍历理论代替排队论。本书的读者对象为高年级学生、科研人员和工程技术人员，对数学、统计、经济等相前专业的学生尤其适用。

FOREWORD PREFACE Patrick Billingsley 1925- 2011 Chapter 1 PROBABILITY 1. BOREL'S NORMAL NUMBER THEOREM, 1 The Unit Interval——The Weak Law of Large Numbers——The Strong Law of Large Numbers——Strong Law Versus Weak—— Length——The Measure Theory of Diophantine Approximation* 2. PROBABILITY MEASURES, 18 Spaces ——Assigning Probabilities——Classes of Sets——Probability Measures——Lebesgue Measure on the Unit Interval——Sequence Space* - Constructing σ-Fields* 3. EXISTENCE AND EXTENSION, 39 Construction of the Extension——Uniqueness and the π-λ Theorem——Monotone Classes——Lebesgue Measure on the Unit Interval- Completeness—— Nonmeasurable Sets——Two Impossibility Theorems* 4. DENUMERABLE PROBABILITIES, 53 General Formulas—— Limit Sets-Independent Events——Subfields——The Borel-Cantelelli Lemmas——The Zero-One Law 5. SIMPLE RANDOM VARIABLES, 72 Definition—— Convergence of Random Variables——Independence——Existence of Independent Sequences—— Expected Value——Inequalities 6. THE LAW OF LARGE NUMBERS, 90 The Strong Law——The Weak Law——Bernstein's Theorem——A Refinement of the Second BoreI-Cantelli Lemma 7. GAMBLING SYSTEMS, 98 Gambler's Ruin——Selection Systems——Gambling Policies——Bold Play*——Timid Play* 8. MARKOVCHAINS, 117 Definitions—— Higher-Order Transitions ——An Existence Theorem——Transience and Persistence——Another Criterion for Persistence——Stationary Distributions—— Exponential Convergence*——Optimal Stopping* 9. LARGE DEVIATIONS AND THE LAW OF THE ITERATED LOGARITHM, 154 Moment Generating Functions——Large Deviations —— Chernoff's Theorem*——The Law of the Iterated Logarithm Chapter 2 MEASURE 167 10. GENERAL MEASURES, 167 Classes of Sets—— Conventions Involving ∞ —— Measures—— Uniqueness 11. OUTER MEASURE, 174 Outer Measure——Extension——An Approximation Theorem 12. MEASURES IN EUCLIDEAN SPACE, 181 Lebesgue Measure——Regularity——Specifying Measures on the Line——Specifying Measures in Rk-strange Euclidean Sets* 13. MEASURABLE FUNCTIONS AND MAPPINGS, 192 Measurable Mappings—— Mappings into Rk- Limits and Measurability——Transformations of Measures 14. DISTRIBUTION FUNCTIONS, 198 Distribution Functions——Exponential Distributions——Weak Convergence—— Convergence of Types* —— Extremal Distributions* Chapter 3 INTEGRATION 211 15. THE INTEGRAL, 211 Definition —— Nonnegative Functions—— Uniqueness 16. PROPERTIES OF THE INTEGRAL, 218 Equalities and Inequalities——Integration to the Limit——Integration over Sets—— Densities—— Change of Variable—— Uniform Integrability—— Complex Functions 17. THE INTEGRAL WITH RESPECT TO LEBESGUE MEASURE, 234 The Lebesgue Integral on the Line——The Riemann Integral——The Fundamental Theorem of Calculus——Change of Variable——The Lebesgue Integral in Rk——Stieltjes Integrals 18. PRODUCT MEASURE AND FUBINI'S THEOREM, 245 Product Spaces—— Product Measure—— Fubini's Theorem——Integration by Parts—— Products of Higher Order 19. THE Lp SPACES*, 256 Definitions—— Completeness and Separability—— Conjugate Spaces——Weak Compactness——Some Decision Theory——The Space L2-An Estimation Problem Chapter 4 RANDOM VARIABLES AND EXPECTED VALUES 271 20. RANDOM VARIABLES AND DISTRIBUTIONS, 271 Random Variables and Vectors—— Subfields—— Distributions —— Multidimensional Distributions——Independence——Sequences of Random Variables——Convolution——Convergence in Probability——The Glivenko-Cantelli Theorem* 21. EXPECTED VALUES, 291 Expected Value as Integral——Expected Values and Limits—— Expected Values and Distributions—— Moments——Inequalities——Joint Integrals——Independence and Expected Value—— Moment Generating Functions 22. SUMS OF INDEPENDENT RANDOM VARIABLES, 300 The Strong Law of Large Numbers——The Weak Law and Moment Generating Functions——Kolmogorov's Zero-One Law—— Maximal Inequalities—— Convergence of Random Series——Random Taylor Series* 23. THE POISSON PROCESS, 316 Characterization of the Exponential Distribution——The Poisson Process——The Poisson Approximation——Other Characterizations of the Poisson Process——Stochastic Processes 24. THE ERGODIC THEOREM*, 330 Measure-Preserving Transformations—— Ergodicity—— Ergodicity of Rotations——Proof of the Ergodic Theorem——The Continued-Fraction Transformation—— Diophantine Approximation Chapter 5 CONVERGENCE OF DISTRIBUTIONS 349 25. WEAK CONVERGENCE, 349 Definitions—— Uniform Distribution Modulo 1 * ——Convergence in Distribution——Convergence in Probability——Fundamental Theorems——Helly's Theorem——Integration to the Limit 26. CHARACTERISTIC FUNCTIONS, 365 Definition —— Moments and Derivatives—— Independence——Inversion and the Uniqueness Theorem——The Continuity Theorem—— Fourier Series* 27. THE CENTRAL LIMIT THEOREM, 380 Identically Distributed Summands——The Lindeberg and Lyapounov Theorems——Dependent Variables* 28. INFINITELY DIVISIBLE DISTRIBUTIONS*, 394 Vague Convergence——The Possible Limits——Characterizing the Limit 29. LIMIT THEOREMS IN Rk, 402 The Basic Theorems—— Characteristic Functions—— Normal Distributions in Rk——The Central Limit Theorem 30. THE METHOD OF MOMENTS*, 412 The Moment Problem——Moment Generating Functions——Central Limit Theorem by Moments——Application to Sampling Theory——Application to Number Theory Chapter 6 DERIVATIVES AND CONDITIONAL PROBABILITY 425 31. DERIVATIVES ON THE LINE*, 425 The Fundamental Theorem of Calculus——Derivatives of Integrals——Singular Functions——Integrals of Derivatives——Functions of Bounded Variation 32. THE RADON-NIKODYM THEOREM, 446 Additive Set Functions——The Hahn Decomposition——Absolute Continuity and Singularity——The Main Theorem 33. CONDITIONAL PROBABILITY, 454 The Discrete Case——The General Case——Properties of Conditional Probability—— Difficulties and Curiosities—— Conditional Probability Distributions 34. CONDITIONAL EXPECTATION, 472 Definition—— Properties of Conditional Expectation——Conditional Distributions and Expectations—— Sufficient Subfields* —— Minimum-Variance Estimation* 35. MARTINGALES, 487 Definition —— Su bmartingales—— Gambling —— Functions of Martingales—— Stopping Times—— Inequalities—— Convergence Theorems——Applications: Derivatives—— Likelihood Ratios—— Reversed Martingales——Applications: de Finetti's Theorem——Bayes Estimation——A Central Limit Theorem* Chapter 7 STOCHASTIC PROCESSES 513 36. KOLMOGOROV'S EXISTENCE THEOREM, 513 Stochastic Processes—— Finite-Dimensional Distributions—— Product Spaces—— Kolmogorov's Existence Theorem——The Inadequacy of RT-A Return to Ergodic Theory——The Hewitt-Savage Theorem* 37. BROWNIAN MOTION, 530 Definition ——Continuity of Paths—— Measurable Processes——Irregularity of Brownian Motion Paths——The Strong Markov Property——The Reflection Principle——Skorohod Embedding ——I nvariance* 38. NONDENUMERABLE PROBABILITIES, 558 Introduction —— Definitions—— Existence Theorems——Consequences of Separability* APPENDIX NOTES ON THE PROBLEMS BIBLIOGRAPHY INDEX

Patrick Billingsley是芝加哥大学统计学和数学教授。他是《管理和经济类适用的统计学》（与Watson等人合作）、《统计推断要义》（与D.L.Huntsberger合作）、《概率测度的收敛性》等书的作者，曾任美国数理统计学会的《概率年刊》主编，他从普林斯顿大学获得哲学博士。

暂无其它内容！

暂时还没有人为这本书评论！