《測度理論概率導論（第2版）（英文版）》主
要介紹了測度理論方面的基礎知識，內容大部分來自
作者的課堂筆記，作者羅薩斯已深入研究概率論多年
，並取得了一定的成果。本書適合作為測度理論和概
率課程的輔助教材，也可以作為分析學、數學及其他
專業學生的課外讀物。

Pictured on the Cover
Preface to First Edition
Preface to Second Edition
CHAPTER 1 Certain Classes of Sets, Measurability, and Pointwise Approximation
1.1 Measurable Spaces
1.2 Product Measurable Spaces
1.3 Measurable Functions and Random Variables
CHAPTER 2 Definition and Construction of a Measure and its Basic Properties
2.1 About Measures in General, and Probability Measures in Particular
2.2 Outer Measures
2.3 The Caratheodory Extension Theorem
2.4 Measures and (Point) Functions
CHAPTER 3 Some Modes of Convergence of Sequences of Random Variables and their Relationships
3.1 Almost Everywhere Convergence and Convergence in Measure
3.2 Convergence in Measure is Equivalent to Mutual Convergence in Measure
CHAPTER 4 The Integral of a Random Variable and its Basic Properties
4.1 Definition of the Integral
4.2 Basic Properties of the Integral
4.3 Probability Distributions
CHAPTER 5 Standard Convergence Theorems, The Fubini Theorem
5.1 Standard Convergence Theorems and Some of Their Ramifications
5.2 Sections, Product Measure Theorem, the Fubini Theorem
5.2.1 Preliminaries for the Fubini Theorem
CHAPTER 6 Standard Moment and Probability Inequalities, Convergence in the rth Mean and its Implications
6.1 Moment and Probability Inequalities
6.2 Convergence in the rth Mean, Uniform Continuity, Uniform Integrability, and Their Relationships
CHAPTER 7 The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and the Radon-Nikodym Theorem
7.1 The Hahn-Jordan Decomposition Theorem
7.2 The Lebesgue Decomposition Theorem
7.3 The Radon-Nikodym Theorem
CHAPTER 8 Distribution Functions and Their Basic Properties, Helly-Bray Type Results
8.1 Basic Properties of Distribution Functions
8.2 Weak Convergence and Compactness of a Sequence of Distribution Functions
8.3 Helly-Bray Type Theorems for Distribution Functions
CHAPTER 9 Conditional Expectation and Conditional Probability, and Related Properties and Results
9.1 Definition of Conditional Expectation and Conditional Probability
9.2 Some Basic Theorems About Conditional Expectations and Conditional Probabilities
9.3 Convergence Theorems and Inequalities for Conditional Expectations
9.4 Further Properties of Conditional Expectations and Conditional Probabilities
CHAPTER 10 Independence
10.1 Independence of Events, σ-Fields, and Random Variables
10.2 Some Auxiliary Results
10.3 Proof of Theorem 1 and of Lemma 1 in Chapter 9
CHAPTER 11 Topics from the Theory of Characteristic Functions
11.1 Definition of the Characteristic Function of a Distribution and Basic Properties
11.2 The Inversion Formula
11.3 Convergence in Distribution and Convergence of Characteristic Functions--The Paul Ltvy Continuity Theorem
11.4 Convergence in Distribution in the Multidimensional Case-The Cramtr-Wold Device
11.5 Convolution of Distribution Functions and Related Results
11.6 Some Further Properties of Characteristic Functions
11.7 Applications to the Weak Law of Large Numbers and the Central Limit Theorem
11.8 The Moments of a Random Variable Determine its Distribution
11.9 Some Basic Concepts and Results from Complex Analysis Employed in the Proof of Theorem 11
CHAPTER 12 The Central Limit Problem: The Centered Case
12.1 Convergence to the Normal Law (Central Limit Theorem, CLT)
12.2 Limiting Laws of L(Sn) Under Conditions (C)
12.3 Conditions for the Central Limit Theorem to Hold
12.4 Proof of Results in Section 12.2
CHAPTER 13 The Central Limit Problem: The Noncentered Case
13.1 Notation and Preliminary Discussion
13.2 Limiting Laws of L(Sn) Under Conditions (C")
13.3 Two Special Cases of the Limiting Laws of L(Sn)
CHAPTER 14 Topics from Sequences of Independent Random Variables
14.1 Kolmogorov Inequalities
14.2 More Important Results Toward Proving the Strong Law of Large Numbers
14.3 Statement and Proof of the Strong Law of Large Numbers
14.4 A Version of the Strong Law of Large Numbers for Random Variables with Infinite Expectation
14.5 Some Further Results on Sequences of Independent Random Variables
CHAPTER 15 Topics from Ergodic Theory
15.1 Stochastic Process, the Coordinate Process, Stationary Process, and Related Results
15.2 Measure-Preserving Transformations, the Shift Transformation, and Related Results
15.3 Invariant and Almost Sure Invariant Sets Relative to a Transformation, and Related Results
15.4 Measure-Preserving Ergodic Transformations, Invariant Random Variables Relative to a Transformation, and Related Results
15.5 The Ergodic Theorem, Preliminary Results
15.6 Invariant Sets and Random Variables Relative to a Process, Formulation of the Ergodic Theorem in Terms of Stationary Processes, Ergodic Processes
CHAPTER 16 Two Cases of Statistical Inference: Estimation of a Real-Valued Parameter, Nonparametric Estimation of a Probability Density Function
16.1 Construction of an Estimate of a Real-Valued Parameter
16.2 Construction of a Strongly Consistent Estimate of a Real-Valued Parameter
16.3 Some Preliminary Results
16.4 Asymptotic Normality of the Strongly Consistent Estimate
16.5 Nonparametric Estimation of a Probability Density Function
16.6 Proof of Theorems 3-5
APPENDIX A Brief Review of Chapters 1-16
APPENDIX B Brief Review of Riemann-Stieltjes Integral
APPENDIX C Notation and Abbreviations
Selected References
Index