# An Introduction to Mathematical Analysis for Economic Theory and Econometrics

Princeton University Press, Feb 17, 2009 - Business & Economics - 688 pages

Providing 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 self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra.

• Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers
• Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem
• Focuses on examples from econometrics to explain topics in measure theory

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### Contents

 Preface Users Guide Notation CHAPTER 1 CHAPTER2 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 Index Copyright