基本介绍

内容简介

《实分析及其在经济学中的应用(英文版)》由世界图书出版公司北京公司出版。

作者简介

作者：（美国）欧克（Efe A.Ok）

图书目录

Preface Prerequisites Basic Conventions PART Ⅰ SET THEORY CHAPTER A Preliminaries of Real Analysis A.1 Elements of Set Theory A.1.1 Sets A.1.2 Relations A.1.3 Equivalence Relations A.1.4 Order Relations A.1.5 Functions A.1.6 Sequences， Vectors， and Matrices A.1.7* A Glimpse of Advanced 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 Rearrangement of Infinite Series A.3.6 Infinite Products A.4 Real Functions A.4.1 Basic Definitions A.4.2 Limits， Continuity， 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 90 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 Theory B.4.1 Preference Relations 100 B.4.2 Utility Representation of Complete Preference Relations B.4.3* Utility Representation of Incomplete 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 Open and Closed Sets C.1.3 Convergent Sequences C.1.4 Sequential Characterization of Closed Sets C.1.5 Equivalence of Metrics C.2 Connectedness and Separability C.2.1 Connected Metric Spaces C.2.2 Separable Metric Spaces C.2.3 Applications to Utility Theory C.3 Compactness C.3.1 Basic Definitions and the Heine—Borel Theorem C.3.2 Compactness as a Finite Structure C.3.3 Closed and Bounded Sets C.4 Sequential Compactness C.5 Completeness C.5.1 Cauchy Sequences C.5.2 Complete Metric Spaces： Definition and Examples C.5.3 Completeness versus Closedness C.5.4 Completeness versus Compactness C.6 Fixed Point Theory Ⅰ C.6.1 Contractions C.6.2 The Banach Fixed Point Theorem C.6.3* Generalizations of the Banach Fixed Point Theorem C.7 Applications to Functional Equations C.7.1 Solutions of Functional Equations C.7.2 Picard's E：astence Theorems C.8 Products of Metric Spaces C.8.1 Finite Products C.8.2 Countably Infinite Products CHAPTER D Continuity Ⅰ D.1 Continuity of Functions D.1.1 Definitions and Examples D.1.2 Uniform Continuity D.1.3 Other Continuity Concepts D.1.4* Remarks on the Differentiability of Real Functions D.1.5 A Fundamental Characterization of Continuity D.1.6 Homeomorphisms D.2 Continuity and Connectedness D.3 Continuity and Compactness D.3.1 Continuous Image of a Compact Set D.3.2 The Local—to—Global Method D.3.3 Weierstrass’ Theorem D.4 Semicontinuity D.5 ADDlications D.5.1* Caristi’s Fixed Point Theorem D.5.2 Continuous Representation of a Preference Relation D.5.3* Cauchy’s Functional Equations： Additivity on Rn D.5.4* Representation of Additive Preferences D.6 CB（T） and Uniform Convergence D.6.1 The Basic Metric Structure of CB（T） D.6.2 Uniform Convergence D.6.3* The Stone—Weierstrass Theorem and Separability of C（T） D.6.4* The Arzela—Ascoli Theorem D.7* Extension of Continuous Functions D.8 Fixed Point Theory Ⅱ D.8.1 The Fixed Point Property D.8.2 Retracts D.8.3 The Brouwer Fixed Point Theorem D.8.4 Applications CHAPTER E Continuity Ⅱ PART Ⅲ ANALYSIS ON LINEAR SPACES CHAPTER F Linear Spaces CHAPTER G Convexity CHAPTER H Economic Applications PART Ⅳ ANALYSIS ON METRIC／NORMED LINEAR SPACES Hints for Selected Exercises References Glossary of Selected Symbols Index