An Introduction to Mathematical Analysis for Economic Theory and EconometricsProviding an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is selfcontained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra.

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Contents
29 Tarskis Lattice FixedPoint Theorem and Stable Matchings  
210 Finite and Infinite Sets  
211The Axiom of Choice and Some Equivalent Results  
68The Metric Completion Theorem  
69The Lebesgue Measure Space  
610Bibliography  
CHAPTER 7  
73 Good Sets Arguments and Measurability  
74Two 01 Laws  
75Dominated Convergence Uniform Integrability and Continuity of the Integral  
76 The Existence of Nonatomic Countably Additive Probabilities  
212Revealed Preference and Rationalizability  
213Superstructures  
214Bibliography  
215EndofChapter Problems  
CHAPTER 3  
CHAPTER4  
49Lipschitz and Uniform Continuity  
410Correspondences and the Theorem of the Maximum  
411 Banachs Contraction Mapping Theorem  
412 Connectedness  
413Bibliography  
CHAPTER 5  
58Separation and the KuhnTucker Theorem  
59 Interpreting Lagrange Multipliers  
510Differentiability and Concavity  
511FixedPoint Theorems and General Equilibrium Theory  
512FixedPoint Theorems for Nash Equilibria and Perfect Equilibria  
513Bibliography  
CHAPTER 6  
63 the Space of Cumulative Distribution Functions  
64 Approximation in CM when M Is Compact  
65Regression Analysis as Approximation Theory  
66Countable Product Spaces and Sequence Spaces  
67Defining Functions Implicitly and by Extension  
77Transition Probabilities Product Measures and Fubinis Theorem  
78Seriously Nonmeasurable Sets and Intergenerational Equity  
79Null Sets Completions ofσFields and Measurable Optima  
710Convergence in Distribution and Skorohods Theorem  
711Complements and Extras  
712Appendix on Lebesgue Integration  
713 Bibliography  
CHAPTER 8  
84Regression Analysis  
85 Signed Measures Vector Measures and Densities  
86Measure Space Exchange Economies  
87Measure Space Games  
Representations and Separation  
89 Weak Convergence in LpΩ P p1  
810Optimization of Nonlinear Operators  
811A Simple Case of Parametric Estimation  
812Complements and Extras  
813Bibliography  
CHAPTER 9  
CHAPTER10  
CHAPTER 11  