概率与测度论
2007-9
人民邮电
[美]RobertB.Ash
516
无
本书是测度论和概率论领域的名著，行文流畅，主线清晰，材料取舍适当，内容包括测度和积分论、泛函分析、条件概率和期望、强大数定理和鞅论、中心极限定理、遍历定理以及布朗运动和随机积分等，全书各节都附有习题，而且在书后提供了大部分习题的详细解答。 本书可作为相关专业高年级本科生或研究生的双语教材，适合作为一学年的教学内容，也可选用其中部分章节用作一学期的教学内容或参考书。
Robert B.Ash，伊利诺大学数学系教授。世界著名数学家，研究领域包括：信息理论、代数、拓扑、概率论、泛函分析等。主要著作有Measure，Integration and Functional Analysis和Information Theory等。
1 Fundamentals of Measure and Integration Theory 1.1 Introduction 1.2 Fields, o-Fields, and Measures 1.3 Extension of Measures 1.4 Lebesgue-Stieltjes Measures and Distribution Functi 1.5 Measurable Functions and Integration 1.6 Basic Integration Theorems 1.7 Comparison of Lebesgue and Riemann Integrals2 Further Results in Measure and Integration Theory 2.1 Introduction 2.2 Radon-Nikodym Theorem and Related Results 2.3 Applications to Real Analysis 2.4 Lp Spaces 2.5 Convergence of Sequences of Measurable Functions 2.6 Product Measures and Fubini's Theorem 2.7 Measures on Infinite Product Spaces 2.8 Weak Convergence of Measures 2.9 References3 Introduction to Functional Analysis 3.1 Introduction 3.2 Basic Properties of Hilbert Spaces 3.3 Linear Operators on Normed Linear Spaces 3.4 Basic Theorems of Functional Analysis 3.5 References4 Basic Concepts of Probability 4.1 Introduction 4.2 Discrete Probability Spaces 4.3 Independence 4.4 Bernoulli Trials 4.5 Conditional Probability 4.6 Random Variables 4.7 Random Vectors 4.8 Independent Random Variables 4.9 Some Examples from Basic Probability 4.10 Expectation 4.11 Infinite Sequences of Random Variables 4.12 References5 Conditional Probability and Expectation 5.1 Introduction 5.2 Applications 5.3 The General Concept of Conditional Probability and Expectation 5.4 Conditional Expectation Given a o-Field 5.5 Properties of Conditional Expectation 5.6 Regular Conditional Probabilities6 Strong Laws of Large Numbers and Martingale Theory 6.1 Introduction 6.2 Convergence Theorems 6.3 Martingales 6.4 Martingale Convergence Theorems 6.5 Uniform Integrability 6.6 Uniform Integrability and Martingale Theory 6.7 Optional Sampling Theorems 6.8 Applications of Martingale Theory 6.9 Applications to Markov Chains 6.10 References7 The Central Limit Theorem 7.1 Introduction 7.2 The Fundamental Weak Compactness Theorem 7.3 Convergence to a Normal Distribution……8 Ergodic Theory9 Brownian Motion and Stochastic IntegralsAppendicesBibliographySolutions to ProblemsIndex
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五折买下,进一步学习概率,基于测度论.
虽然表面有点脏，不过书的内容没的说，很好
书送的很快啊，服务业不错，不过请运送的时候注意一点哦，我看书上有点灰
经典之作，较易上手
作为第一个评论此书的人，我不推荐这本书，虽然这本书给出了不少习题的解答，但内容达不到一般测度论的广度和深度。如果做金融随机分析，不如直接看金融数学的书，可以节省很多时间，如果搞概率研究的，还是看rudin的realandcomplexanalysis好一点！
深入浅出，比中文翻译的看起来容易很多，讲的很详细，很好
好书 难度也不低 可供数学系参考