《实分析及其在经济学中的应用》是一部理想的教程和参考资料，填补了众多实分析教程不能帮助学生学习经济理论，帮助研究生接近经济学。本书通篇都仅仅围绕着经济学展开讲述实分析，除了实分析的普通论题，书中讨论了阶理论、凸分析、优化、对应理论、线性和非线性泛函分析、不动点理论、动态规划和变分法。作者欧克通过应用案例，从包括个人决策理论和博弈，福利经济学、信息论、一般平衡和金融、跨期经济学这些经济理论出发补充讲述了数学进展。除了讲述在经济学中的直接应用以外，还包括了大量的不动点理论和泛函方程和最优化理论中的应用。

Preface

Prerequisites

Basic Conventions

PART Ⅰ SET THEORY

CHAPTER A Preliminaries of Real Analysis

A.1 Elements ofSet Theory

A.1.1 Sets

A.1.2 Relations

A.1.3 Equivalence Relations

A.1.4 O0rder Relations

A.1.5 Functions

A.1.6 Sequences, Vectors, and Matrices

A.1.7 A Glimpse ofAdvanced Set Theory: The Axiom of Choice

A.2 Real Numbers

A.2.1 Ordered Fields

A.2.2 Natural Numbers, Integers, and Rationals

A.2.3 Real Numbers

A.2.4 Intervals and R

A.3 Real Sequences

A.3.1 Convergent Sequences

A.3.2 Monotonic Sequences

A.3.3 Subsequential Limits

A.3.4 Infinite Series

A.3.5 Rear.rangement oflnfinite Series

A.3.6 Infinite Products

A.4 Real Functions

A.4.1 Basic Definitions

A.4.2 Limits, ContinLuty, and Differentiation

A.4.3 Riemann Integration

A.4.4 Exponential, Logarithmic, and Trigonometric Functions

A.4.5 Concave and Convex Functions

A.4.6 Quasiconcave and Quasiconvex Functions

CHAPTER B Countability

B.1 Countable and Uncountable Sets

B.2 Losets and Q

B.3 Some More Advanced Set Theory

B.3.1 The Cardinality Ordering

B.3.2 The Well-Ordering Principle

B.4 Application: Ordinal utility Theor）r

B.4.1 Preference Relations

B.4.2 Utilitv ReDresentation of Complete Preference Relations

B.4.3 Utility Representation oflncomplete Preference Relations

PART Ⅱ ANALYSIS ON METRIC SPACES

CHAPTER C Metric Spaces

C.1 Basic Notions

C.1.1 Metric Spaces: Definition and Examples

C.1.2 0pen and Closed Sets

C.1.3 Convergent Sequences

……

PART Ⅲ ANALYSIS ON LINEAR SPACES

PART Ⅳ ANALYSIS ON METRIC/NORMED LINEAR SPACES

Hints for Selected Exercises

References

Clossary of Selected Symbols

Index