New York University
Department of Economics

		Real Analysis with Economic Applications Efe A. Ok Book Description and Endorsements Table of Contents
Chapter A: Preliminaries of Real Analysis Addenda Corrections: Typos
	Chapter B: Countability Addenda: Section B.4.3 (Rewritten) Corrections: Typos
	Chapter C: Metric Spaces Addenda Corrections: Typos
	Chapter D: Continuity I Addenda: The Ekeland Variational Principle / Proof of Brouwer’s Fixed Point Theorem / Motzkin’s Characterization of Convex Sets Corrections: The Thoughtful Correction of Footnote 47 by Douglas Bridges / Typos
	Chapter E: Continuity II Addenda Corrections Chapter F: Linear Spaces Addenda Corrections: Typos Chapter G: Convexity Addenda Corrections: Typos Chapter H: Economic Applications Addenda Corrections Chapter I: Metric Linear Spaces Addenda Corrections: Typos Chapter J: Normed Linear Spaces Addenda Corrections Chapter K: Differential Calculus Addenda: On the Existence of Approximate Stationary Points Corrections: Typos Hints to Selected Exercises Addenda Corrections: Correction to Exercise F.3 References

PROBABILITY THEORY with ECONOMIC APPLICATIONS Efe A. Ok
	Preface (TBW) Table of Contents
	Chapter A: Preliminaries
	Chapter B: Probability via Measue Theory Event Spaces / Probability Spaces / Constructing of Probability Spaces / The Sierpinski Class Lemma / Random Variables Chapter C: Expectation via the Lebesgue Integral The Expectation Functional / Application: First-Order Stochastic Dominance / Almost Sure Convergence Theorems / The Lebesgue Integral / Elementary Inequalities / Spaces of Integrable Random Variables / Probability Measures Induced by Expectations Chapter D: Expectation via the Stieltjes Integral The Stieltjes Integral / The Expectation Functional as a Stieltjes Integral / Integration by Parts / Stochastic Dominance Theory / Economic Applications of Stochastic Dominance Theory Chapter E: Weak Convergence Weak Convergence of Probability Measures / Convergence of Random Variables / The Prokhorov Metrization / Properties of P(X) / An Alternative Metrization of P(X) Chapter F: Applications to Decision-Making under Risk and Uncertainty The Expected Utility Theorem / Decision-Making Under Uncertainty Chapter G: Stochastic Independence Independence of Classes of Events / Independence of Random Variables / Finite Products of Probability Spaces / Application: Nash Equilibrium in Mixed Strategies / Infinite Products of Probability Spaces Chapter H: A Primer on Probability Limit Theorems Preliminaries / Laws of Large Numbers / The Borel-Cantelli Lemmas / Convergence of Series of Random Variables / Kolmogorov’s 0-1 Law Chapter I: Conditional Expectation Conditional Expectation / Properties of Conditional Expectation Chapter J: Martingales Martingales / Stopped Martingales / The Martingale Convergence Theorems / Applications Appendix 1: Metric Spaces Appendix 2: Linear and Normed Linear Spaces Hints to Selected Exercises References

Elements of ORDER THEORY Efe A. Ok
	Preface (TBW) Table of Contents
	Chapter 1: Preordered Sets, Posets and Lattices Binary Relations / Equivalence Relations / Order Relations / Representation through Complete Preorders / Maxima and Minima / Parameters of Posets / Suprema and Infima / Lattices / Supermodularity
	Chapter 2: Order-Preserving Maps and Isomorphisms Order-Preserving Functions / Galois Connections / Order-Preserving Correspondences / An Application to Optimization Theory Chapter 3: Mobius Functions Motivation: Inversion Problems on Posets / Incidence Algebras / Mobius Functions / Application: Preferences for Flexibility / An Application to Game Theory Chapter 4: Zorn’s Lemma and its Applications The Axiom of Choice / The Hausdorff Maximal Principle / An Application to Optimization Theory / Zorn’s Lemma / Applications of Zorn’s Lemma / Digression: Pathological Consequences of Zorn’s Lemma / The Well-Ordering Principle Chapter 5: Order-Theoretic Fixed Point Theory Fixed Point Theory / Completeness Conditions for Posets / Iterative Fixed Point Theorems / Tarski’s Fixed Point Theorems / Converse of the Knaster-Tarski Theorem / The Abian-Brown Fixed Point Theorem / Fixed Point Theorems for Set-Valued Maps Chapter 6: The Brezis-Browder Ordering Principle and its Applications A Selection of Ordering Principles / Applications to Metric Fixed Point Theory / Applications to Optimization Theory / An Application to Convex Analysis Chapter 7: Completions and Decompositions of Preordered Sets (TBW) Chapter 8: Functional (Utility) Representation of Preorders Preliminaries / Representation through Order-Separability / Representation through Semicontinuity / The Open Gap Lemma / The Debreu-Eilenberg Representation Theorems / Multi-Utility Representation / Continuous Multi-Utility Representation / Finite Multi-Utility Representation Chapter 9: Represesentation of Distributive Lattices Introduction / Ideals and Filters / Representation of Distributive Lattices I / Representation of Distributive Lattices II / Ordered Stone Spaces / Representation of Distributive Lattices III Chapter 10: Advances in Lattice Theory (TBW) Appendix: A Primer on Topological Spaces Topological Spaces / Metric Spaces / The Hausdorff Metric References