作者：(美)M. Loeve著
页数：425页
出版社：世界图书出版公司
出版日期：2019
ISBN：9787519255770
电子书格式：pdf/epub/txt
内容简介
本书被公认为是一套概率论方面的标准经典教科书，供高年级大学生和研究生使用，同时也是概率论和统计学方面研究人员经常使用的参考书。本书把概率论建立在严格的逻辑基础上，理论体系完整。在第4版中增加了距离空间测定、随机游动、布朗运动及不变原理四部分，后两部分尤为精彩。全书除引言外，两卷共分五部分，第1卷包括三部分，涉及概率论的基本概念和数学手段。读者对象：数学及相关专业的研究生。
作者简介
这部两卷集研究生教材的作者M. loève（M. 洛易甫）是美国伯克利大学教授，本书把概率论建立在严格的逻辑基础上，理论体系完整。
目录
VOLUME 1
Ⅰ. INTUITIVE BACKGROUND
1. Events
2. Random events and trials
3. Random variables
Ⅱ. AXIOMS; INDEPENDENCE AND THE BERN ULLI CASE
1. Axioms of the finite case
2. Simple random variables
3. Independence
4. Bernoulli case
5. Axioms for the countable cast
6. Elementary random variable,s
7. Need for nonelementary random wariables
Ⅲ. DEPENDENCE AND CHAINS
1. Conditional probabilities
2. Asymptotically Bernoullian ctse
3. Recurrence
4. Chain dependence
最 5. Types of states and asympto’ti~ l:eh atvior
最 6. Motion of the system
最 7. Stationary chains .
COMPLEMENTS AND DETAILS
PART ONE: NOTIONS OF MEASURE THEORY
CHAPTER I: SETS, SPACES, AND MEASURES
1. SETS, CLASSES, AND FUNCTIONS
1.1 Definitions and notations
1.2 Differences, unions, and intersections
1.3 Sequences and limits
1.4 Indicators of sets
1.5 Fields and a-fields
1.6 Monotone classes
最1.7 Product sets
最1.8 Functions and inverse functions
最1.9 Measurable spaces and functions
最2. TOPOLOGICAL SPACES .
最2.1 Topologies and limits
最2.2 Limit points and compact spaces
最2.3 Countability and metric spaces
最2.4 Linearity and normed spaces
3. ADDITIVE SET FUNCTIONS
3.1 Additivity and continuity
3.2 Decomposition of additive set functions
最4. CONSTRUCTION Of MEASURES ON #-FIELDS
最4.1 Extension of measures
最4.2 Product probabilities
最4.3 Consistent probabilities on Borel fields
最4.4 Lebesgue-Stieltjes measures and distribution functions
COMPLEMENTS AND DETAILS
CHAPTER II: MEASURABLE FUNCTIONS AND INTEGRATION
5. MEASURABLE FUNCTIONS
5.1 Numbers
5.2 Numerical functions
5.3 Measurable functions
6. MEASURE AND CONVERGENCES
6.1 Definitions and general properties
6.2 Convergence almost everywhere
6.3 Convergence in measure
7. INTEGRATION
7.1 Integrals
7.2 Convergence theorems
8. INDEFINITE INTEGRALS; ITERATED INTEGRALS
8.1 Indefinite integrals and Lcbcsgue decomposition
8.2 Product measures and iterated integrals
最8.3 Iterated integrals and infinite product spaces
……
PART TWO: GENERAL CONCEPTS AND TOOLS OF PROBALITY THEORY
PART THREE: INDEPENDENCE
BIBLIOGRAPHY
INDEX
VOLUME Ⅱ
DEPENDENCE
ELEMENTS OF RANDOM ANALYSIS
BIBLIOGRAPHY
INDEX
Ⅰ. INTUITIVE BACKGROUND
1. Events
2. Random events and trials
3. Random variables
Ⅱ. AXIOMS; INDEPENDENCE AND THE BERN ULLI CASE
1. Axioms of the finite case
2. Simple random variables
3. Independence
4. Bernoulli case
5. Axioms for the countable cast
6. Elementary random variable,s
7. Need for nonelementary random wariables
Ⅲ. DEPENDENCE AND CHAINS
1. Conditional probabilities
2. Asymptotically Bernoullian ctse
3. Recurrence
4. Chain dependence
最 5. Types of states and asympto’ti~ l:eh atvior
最 6. Motion of the system
最 7. Stationary chains .
COMPLEMENTS AND DETAILS
PART ONE: NOTIONS OF MEASURE THEORY
CHAPTER I: SETS, SPACES, AND MEASURES
1. SETS, CLASSES, AND FUNCTIONS
1.1 Definitions and notations
1.2 Differences, unions, and intersections
1.3 Sequences and limits
1.4 Indicators of sets
1.5 Fields and a-fields
1.6 Monotone classes
最1.7 Product sets
最1.8 Functions and inverse functions
最1.9 Measurable spaces and functions
最2. TOPOLOGICAL SPACES .
最2.1 Topologies and limits
最2.2 Limit points and compact spaces
最2.3 Countability and metric spaces
最2.4 Linearity and normed spaces
3. ADDITIVE SET FUNCTIONS
3.1 Additivity and continuity
3.2 Decomposition of additive set functions
最4. CONSTRUCTION Of MEASURES ON #-FIELDS
最4.1 Extension of measures
最4.2 Product probabilities
最4.3 Consistent probabilities on Borel fields
最4.4 Lebesgue-Stieltjes measures and distribution functions
COMPLEMENTS AND DETAILS
CHAPTER II: MEASURABLE FUNCTIONS AND INTEGRATION
5. MEASURABLE FUNCTIONS
5.1 Numbers
5.2 Numerical functions
5.3 Measurable functions
6. MEASURE AND CONVERGENCES
6.1 Definitions and general properties
6.2 Convergence almost everywhere
6.3 Convergence in measure
7. INTEGRATION
7.1 Integrals
7.2 Convergence theorems
8. INDEFINITE INTEGRALS; ITERATED INTEGRALS
8.1 Indefinite integrals and Lcbcsgue decomposition
8.2 Product measures and iterated integrals
最8.3 Iterated integrals and infinite product spaces
……
PART TWO: GENERAL CONCEPTS AND TOOLS OF PROBALITY THEORY
PART THREE: INDEPENDENCE
BIBLIOGRAPHY
INDEX
VOLUME Ⅱ
DEPENDENCE
ELEMENTS OF RANDOM ANALYSIS
BIBLIOGRAPHY
INDEX
