概率與測度論

內(nèi)容概要

本書是測度論和概率論領(lǐng)域的名著，行文流暢，主線清晰，材料取舍適當(dāng)，內(nèi)容包括測度和積分論、泛函分析、條件概率和期望、強(qiáng)大數(shù)定理和鞅論、中心極限定理、遍歷定理以及布朗運(yùn)動和隨機(jī)積分等，全書各節(jié)都附有習(xí)題，而且在書后提供了大部分習(xí)題的詳細(xì)解答?！　”緯勺鳛橄嚓P(guān)專業(yè)高年級本科生或研究生的雙語教材，適合作為一學(xué)年的教學(xué)內(nèi)容，也可選用其中部分章節(jié)用作一學(xué)期的教學(xué)內(nèi)容或參考書。

作者簡介

Robert B.Ash，伊利諾大學(xué)數(shù)學(xué)系教授。世界著名數(shù)學(xué)家，研究領(lǐng)域包括：信息理論、代數(shù)、拓?fù)?、概率論、泛函分析等。主要著作有Measure，Integration and Functional Analysis和Information Theory等。

書籍目錄

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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