| Preface | p. xi |
| User's Guide | p. xiii |
| Notation | p. xix |
| Logic | p. 1 |
| Statements, Sets, Subsets, and Implication | p. 1 |
| Statements and Their Truth Values | p. 3 |
| Proofs, a First Look | p. 6 |
| Logical Quantifiers | p. 9 |
| Taxonomy of Proofs | p. 11 |
| Set Theory | p. 15 |
| Some Simple Questions | p. 16 |
| Notation and Other Basics | p. 17 |
| Products, Relations, Correspondences, and Functions | p. 21 |
| Equivalence Relations | p. 26 |
| Optimal Choice for Finite Sets | p. 28 |
| Direct and Inverse Images, Compositions | p. 33 |
| Weak and Partial Orders, Lattices | p. 39 |
| Monotonic Changes in Optima: Supermodularity and Lattices | p. 42 |
| Tarski's Lattice Fixed-Point Theorem and Stable Matchings | p. 49 |
| Finite and Infinite Sets | p. 56 |
| The Axiom of Choice and Some Equivalent Results | p. 62 |
| Revealed Preference and Rationalizability | p. 64 |
| Superstructures | p. 68 |
| Bibliography | p. 69 |
| End-of-Chapter Problems | p. 70 |
| The Space of Real Numbers | p. 72 |
| Why We Want More Than the Rationals | p. 72 |
| Basic Properties of Rationals | p. 73 |
| Distance, Cauchy Sequences, and the Real Numbers | p. 75 |
| The Completeness of the Real Numbers | p. 82 |
| Examples Using Completeness | p. 87 |
| Supremum and Infimum | p. 90 |
| Summability | p. 92 |
| Products of Sequences and ex | p. 99 |
| Patience, Lim inf, and Lim sup | p. 101 |
| Some Perspective on Completing the Rationals | p. 104 |
| Bibliography | p. 105 |
| The Finite-Dimensional Metric Space of Real Vectors | p. 106 |
| The Basic Definitions for Metric Spaces | p. 107 |
| Discrete Spaces | p. 113 |
| Rl as a Normed Vector Space | p. 114 |
| Completeness | p. 120 |
| Closure, Convergence, and Completeness | p. 124 |
| Separability | p. 128 |
| Compactness in Rl | p. 129 |
| Continuous Functions on Rl | p. 136 |
| Lipschitz and Uniform Continuity | p. 143 |
| Correspondences and the Theorem of the Maximum | p. 144 |
| Banach's Contraction Mapping Theorem | p. 154 |
| Connectedness | p. 167 |
| Bibliography | p. 171 |
| Finite-Dimensional Convex Analysis | p. 172 |
| The Basic Geometry of Convexity | p. 173 |
| The Dual Space of Rl | p. 181 |
| The Three Degrees of Convex Separation | p. 184 |
| Strong Separation and Neoclassical Duality | p. 186 |
| Boundary Issues | p. 194 |
| Concave and Convex Functions | p. 199 |
| Separation and the Hahn-Banach Theorem | p. 209 |
| Separation and the Kuhn-Tucker Theorem | p. 214 |
| Interpreting Lagrange Multipliers | p. 228 |
| Differentiability and Concavity | p. 232 |
| Fixed-Point Theorems and General Equilibrium Theory | p. 239 |
| Fixed-Point Theorems for Nash Equilibria and Perfect Equilibria | p. 245 |
| Bibliography | p. 258 |
| Metric Spaces | p. 259 |
| The Space of Compact Sets and the Theorem of the Maximum | p. 260 |
| Spaces of Continuous Functions | p. 272 |
| D(R), the Space of Cumulative Distribution Functions | p. 293 |
| Approximation in C(M) when M Is Compact | p. 297 |
| Regression Analysis as Approximation Theory | p. 304 |
| Countable Product Spaces and Sequence Spaces | p. 311 |
| Defining Functions Implicitly and by Extension | p. 321 |
| The Metric Completion Theorem | p. 331 |
| The Lebesgue Measure Space | p. 335 |
| Bibliography | p. 343 |
| End-of-Chapter Problems | p. 344 |
| Measure Spaces and Probability | p. 355 |
| The Basics of Measure Theory | p. 356 |
| Four Limit Results | p. 370 |
| Good Sets Arguments and Measurability | p. 388 |
| Two 0-1 Laws | p. 397 |
| Dominated Convergence, Uniform Integrability, and Continuity of the Integral | p. 400 |
| The Existence of Nonatomic Countably Additive Probabilities | p. 411 |
| Transition Probabilities, Product Measures, and Fubini's Theorem | p. 423 |
| Seriously Nonmeasurable Sets and Intergenerational Equity | p. 426 |
| Null Sets, Completions of s-Fields, and Measurable Optima | p. 430 |
| Convergence in Distribution and Skorohod's Theorem | p. 436 |
| Complements and Extras | p. 440 |
| Appendix on Lebesgue Integration | p. 448 |
| Bibliography | p. 451 |
| The Lp (ohm; F, P) and lp Spaces, p E [1, ?] | p. 452 |
| Some Uses in Statistics and Econometrics | p. 453 |
| Some Uses in Economic Theory | p. 456 |
| The Basics of Lp(ohm; F, P) and lp | p. 458 |
| Regression Analysis | p. 474 |
| Signed Measures, Vector Measures, and Densities | p. 490 |
| Measure Space Exchange Economies | p. 498 |
| Measure Space Games | p. 503 |
| Dual Spaces: Representations and Separation | p. 509 |
| Weak Convergence in Lp (?, F, P), p E [1, ?) | p. 518 |
| Optimization of Nonlinear Operators | p. 522 |
| A Simple Case of Parametric Estimation | p. 528 |
| Complements and Extras | p. 541 |
| Bibliography | p. 550 |
| Probabilities on Metric Spaces | p. 551 |
| Choice under Uncertainty | p. 551 |
| Stochastic Processes | p. 552 |
| The Metric Space (Delta;(M), p) | p. 553 |
| Two Useful Implications | p. 562 |
| Expected Utility Preferences | p. 563 |
| The Riesz Representation Theorem for Delta;(M), M Compact | p. 567 |
| Polish Measure Spaces and Polish Metric Spaces | p. 569 |
| The Riesz Representation Theorem for Polish Metric Spaces | p. 571 |
| Compactness in Delta;(M) | p. 574 |
| An Operator Proof of the Central Limit Theorem | p. 578 |
| Regular Conditional Probabilities | p. 583 |
| Conditional Probabilities from Maximization | p. 589 |
| Nonexistence of rcp's | p. 590 |
| Bibliography | p. 594 |
| Infinite-Dimensional Convex Analysis | p. 595 |
| Topological Spaces | p. 595 |
| Locally Convex Topological Vector Spaces | p. 603 |
| The Dual Space and Separation | p. 606 |
| Filterbases, Filters, and Ultrafilters | p. 610 |
| Bases, Subbases, Nets, and Convergence | p. 612 |
| Compactness | p. 617 |
| Compactness in Topological Vector Spaces | p. 621 |
| Fixed Points | p. 624 |
| Bibliography | p. 626 |
| Expanded Spaces | p. 627 |
| The Basics of *R | p. 628 |
| Superstructures, Transfer, Spillover, and Saturation | p. 632 |
| Loeb Spaces | p. 642 |
| Saturation, Star-Finite Maximization Models, and Compactification | p. 649 |
| The Existence of a Purely Finitely Additive {0, 1}-Valued m | p. 652 |
| Problems and Complements | p. 653 |
| Bibliography | p. 654 |
| Index | p. 655 |
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