An Introduction to Mathematical Analysis for Economic Theory and Econometrics

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

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About the author (2009)

Dean Corbae is the Rex A. and Dorothy B. Sebastian Centennial Professor in Business Administration at the University of Texas at Austin. Maxwell B. Stinchcombe is the E. C. McCarty Centennial Professor of Economics at the University of Texas at Austin. Juraj Zeman is researcher at the National Bank of Slovakia and lecturer in applied mathematics at Comenius University in Bratislava.

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