This is primarily a textbook on mathematical analysis for
graduate students in economics. While there are a large number of
excellent textbooks on this broad topic in the mathematics
literature， most ofthese texts are overly advanced relative to the
needs of the vast majority of economics students and concentrate on
various topics that are not readily helpful for studying economic
theory. Moreover， it seems that most economics students lack the
time or courage to enroll in a math course at the graduate
level. Sometimes this is not even for bad reasons， for only few
math departments offer classes that are designed for the parhcular
needs of economists. Unfortunately，more often than not， the
consequent lack ofmathematical background cre-ates problems for the
students at a later stage of their education， since an exceedingly
large fraction ofeconomic theory is impenetrable without some
rigorous background in real analysis. The present text aims at
providing a remedy for this inconvenient situation.
目錄：
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 METRICNORMED LINEAR SPACES
Hints for Selected Exercises
References
Clossary of Selected Symbols
Index
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