Real analysis with economic applications:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2007
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| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Physical Description: | XXX, 802 S. graph. Darst. |
| ISBN: | 0691117683 9780691117683 |
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MARC
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| 245 | 1 | 0 | |a Real analysis with economic applications |c Efe A. Ok |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2007 | |
| 300 | |a XXX, 802 S. |b graph. Darst. | ||
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| 650 | 7 | |a Matemática aplicada (economia) |2 larpcal | |
| 650 | 4 | |a Mathématiques économiques | |
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| 650 | 4 | |a Economics, Mathematical | |
| 650 | 4 | |a Mathematical analysis | |
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| adam_text | REAL ANALYSIS WITH ECONOMIC APPLICATIONS EFE A. OK PRINCETON UNIVERSITY
PRESS I PRINCETON AND OXFORD CONTENTS PREFACE XVII PREREQUISITES XXVII
BASIC CONVENTIONS XXIX PART I SET THEORY 1 CHAPTER A PRELIMINARIES OF
REAL ANALYSIS 3 A.I ELEMENTS OF SET THEORY 4 A.I.I SETS 4 A. 1.2
RELATIONS 9 A. 1.3 EQUIVALENCE RELATIONS 11 A.1.4 ORDER RELATIONS 14 A.
1.5 FUNCTIONS 20 A.1.6 SEQUENCES, VECTORS, AND MATRICES 27 A.1.7* A
GLIMPSE OF ADVANCED SET THEORY: THE AXIOM OF CHOICE 29 A.2 REAL NUMBERS
33 A.2.1 ORDERED FIELDS 33 A.2.2 NATURAL NUMBERS, INTEGERS, AND
RATIONALS 37 A.2.3 REAL NUMBERS 39 A.2.4 INTERVALS AND 1 44 A. 3 REAL
SEQUENCES 46 A.3.1 CONVERGENT SEQUENCES 46 A.3.2 MONOTONIC SEQUENCES 50
A.3.3 SUBSEQUENTIAL LIMITS 53 VIN I CONTENTS A.3.4 INFINITE SERIES 56
A.3.5 REARRANGEMENT OF INFINITE SERIES 59 A.3.6 INFINITE PRODUCTS 61 A.4
REAL FUNCTIONS 62 A.4.1 BASIC DEFINITIONS 62 A.4.2 LIMITS, CONTINUITY,
AND DIFFERENTIATION 64 A.4.3 RIEMANN INTEGRATION 69 A.4.4 EXPONENTIAL,
LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS 74 A.4.5 CONCAVE AND CONVEX
FUNCTIONS 77 A.4.6 QUASICONCAVE AND QUASICONVEX FUNCTIONS 80 CHAPTER B
COUNTABILITY 82 B.I COUNTABLE AND UNCOUNTABLE SETS 82 B.2 LOSETSANDQ 90
B.3 SOME MORE ADVANCED SET THEORY 93 B.3.1 THE CARDINALITY ORDERING 93
B.3.2* THE WELL-ORDERING PRINCIPLE 98 B.4 APPLICATION: ORDINAL UTILITY
THEORY 99 B.4.1 PREFERENCE RELATIONS 100 B.4.2 UTILITY REPRESENTATION OF
COMPLETE PREFERENCE RELATIONS 102 B.4.3* UTILITY REPRESENTATION OF
INCOMPLETE PREFERENCE RELATIONS 107 PART II ANALYSIS ON METRIC SPACES
115 CHAPTER C METRIC SPACES 117 C.I BASIC NOTIONS 118 C.I.I METRIC
SPACES: DEFINITION AND EXAMPLES 119 C.1.2 OPEN AND CLOSED SETS 127 C.I.3
CONVERGENT SEQUENCES 132 CONTENTS I IX C.1.4 SEQUENTIAL CHARACTERIZATION
OF CLOSED SETS 134 C.I.5 EQUIVALENCE OF METRICS 136 C.2 CONNECTEDNESS
AND SEPARABILITY 138 C.2.1 CONNECTED METRIC SPACES 138 C.2.2 SEPARABLE
METRIC SPACES 140 C.2.3 APPLICATIONS TO UTILITY THEORY 145 C.3
COMPACTNESS 147 C.3.1 BASIC DEFINITIONS AND THE HEINE-BOREL THEOREM 148
C.3.2 COMPACTNESS AS A FINITE STRUCTURE 151 C.3.3 CLOSED AND BOUNDED
SETS 154 C.4 SEQUENTIAL COMPACTNESS 157 C.5 COMPLETENESS 161 C.5.1
CAUCHY SEQUENCES 161 C.5.2 COMPLETE METRIC SPACES: DEFINITION AND
EXAMPLES 163 C.5.3 COMPLETENESS VERSUS CLOSEDNESS 167 C.5.4 COMPLETENESS
VERSUS COMPACTNESS 171 C.6 FIXED POINT THEORY I 172 C.6.1 CONTRACTIONS
172 C.6.2 THE BANACH FIXED POINT THEOREM 175 C.6.3* GENERALIZATIONS OF
THE BANACH FIXED POINT THEOREM 179 C.7 APPLICATIONS TO FUNCTIONAL
EQUATIONS 183 C.7.1 SOLUTIONS OF FUNCTIONAL EQUATIONS 183 C.7.2 PICARD S
EXISTENCE THEOREMS 187 C.8 PRODUCTS OF METRIC SPACES 192 C.8.1 FINITE
PRODUCTS 192 C.8.2 COUNTABLY INFINITE PRODUCTS 193 CHAPTER D CONTINUITY
I 200 D.I CONTINUITY OF FUNCTIONS 201 D.I.I DEFINITIONS AND EXAMPLES 201
D.I.2 UNIFORM CONTINUITY 208 X I CONTENTS D.I.3 OTHER CONTINUITY
CONCEPTS 210 D.I.4* REMARKS ON THE DIFFERENTIABILITY OF REAL FUNCTIONS
212 D.I.5 A FUNDAMENTAL CHARACTERIZATION OF CONTINUITY 213 D.I.6
HOMEOMORPHISMS 216 D.2 CONTINUITY AND CONNECTEDNESS 218 D.3 CONTINUITY
AND COMPACTNESS 222 D.3.1 CONTINUOUS IMAGE OF A COMPACT SET 222 D.3.2
THE LOCAL-TO-GLOBAL METHOD 223 D.3.3 WEIERSTRASS THEOREM 225 D.4
SEMICONTINUITY 229 D.5 APPLICATIONS 237 D.5.1* CARISTI S FIXED POINT
THEOREM 238 D.5.2 CONTINUOUS REPRESENTATION OF A PREFERENCE RELATION 239
D.5.3* CAUCHY S FUNCTIONAL EQUATIONS: ADDITIVITY ON R 242 D.5.4*
REPRESENTATION OF ADDITIVE PREFERENCES 247 D.6 CB(T) AND UNIFORM
CONVERGENCE 249 D.6.1 THE BASIC METRIC STRUCTURE OF CB(T) 249 D.6.2
UNIFORM CONVERGENCE 250 D.6.3* THE STONE-WEIERSTRASS THEOREM AND
SEPARABILITY OF C(T) 257 D.6.4* THE ARZELA-ASCOLI THEOREM 262
D.7*EXTENSION OF CONTINUOUS FUNCTIONS 266 D.8 FIXED POINT THEORY II 272
D.8.1 THE FIXED POINT PROPERTY 273 D.8.2 RETRACTS 274 D.8.3 THE BROUWER
FIXED POINT THEOREM 277 D.8.4 APPLICATIONS 280 S CHAPTER E CONTINUITY II
283 E.I CORRESPONDENCES 284 E.2 CONTINUITY OF CORRESPONDENCES 287 E.2.1
UPPER HEMICONTINUITY 287 E.2.2 THE CLOSED GRAPH PROPERTY 294 E.2.3 LOWER
HEMICONTINUITY 297 CONTENTS I XI E.2.4 CONTINUOUS CORRESPONDENCES 300
E.2.5* THE HAUSDORFF METRIC AND CONTINUITY 302 E.3 THE MAXIMUM THEOREM
306 E.4 APPLICATION: STATIONARY DYNAMIC PROGRAMMING 311 E.4.1 THE
STANDARD DYNAMIC PROGRAMMING PROBLEM 312 E.4.2 THE PRINCIPLE OF
OPTIMALITY 315 E.4.3 EXISTENCE AND UNIQUENESS OF AN OPTIMAL SOLUTION 320
E.4.4 APPLICATION: THE OPTIMAL GROWTH MODEL 324 E.5 FIXED POINT THEORY
III 330 E.5.1 KAKUTANI S FIXED POINT THEOREM 331 E.5.2* MICHAEL S
SELECTION THEOREM 333 E.5.3* PROOF OF KAKUTANI S FIXED POINT THEOREM 339
E.5.4* CONTRACTIVE CORRESPONDENCES 341 E.6 APPLICATION: THE NASH
EQUILIBRIUM 343 E.6.1 STRATEGIC GAMES 343 E.6.2 THE NASH EQUILIBRIUM 346
E.6.3* REMARKS ON THE EQUILIBRIA OF DISCONTINUOUS GAMES 351 PART III
ANALYSIS ON LINEAR SPACES 355 CHAPTER F LINEAR SPACES 357 F.I LINEAR
SPACES 358 F.I.I ABELIAN GROUPS 358 F.I.2 LINEAR SPACES: DEFINITION AND
EXAMPLES 360 F.I.3 LINEAR.SUBSPACES, AFFINE MANIFOLDS, AND HYPERPLANES
364 F.1.4 SPAN AND AFFINE HULL OF A SET 368 F.I.5 LINEAR AND AFFINE
INDEPENDENCE 370 F.I.6 BASES AND DIMENSION 375 F.2 LINEAR OPERATORS AND
FUNCTIONALS 382 F.2.1 DEFINITIONS AND EXAMPLES 382 F.2.2 LINEAR AND
AFFINE FUNCTIONS 386 XII I CONTENTS F.2.3 LINEAR ISOMORPHISMS 389 F.2.4
HYPERPLANES, REVISITED 392 F.3 APPLICATION: EXPECTED UTILITY THEORY 395
F.3.1 THE EXPECTED UTILITY THEOREM 395 F.3.2 UTILITY THEORY UNDER
UNCERTAINTY 403 F.4* APPLICATION: CAPACITIES AND THE SHAPLEY VALUE 409
F.4.1 CAPACITIES AND COALITIONAL GAMES 410 F.4.2 THE LINEAR SPACE OF
CAPACITIES 412 F.4.3 THE SHAPLEY VALUE 415 CHAPTER G CONVEXITY 422 G.I
CONVEX SETS 423 G.I.I BASIC DEFINITIONS AND EXAMPLES 423 G.1.2 CONVEX
CONES 428 G.I.3 ORDERED LINEAR SPACES 432 G.1.4 ALGEBRAIC AND RELATIVE
INTERIOR OF A SET 436 G.1.5 ALGEBRAIC CLOSURE OF A SET 447 G.I.6
FINITELY GENERATED CONES 450 G.2 SEPARATION AND EXTENSION IN LINEAR
SPACES 454 G.2.1 EXTENSION OF LINEAR FUNCTIONALS 455 G.2.2 EXTENSION OF
POSITIVE LINEAR FUNCTIONALS 460 G.2.3 SEPARATION OF CONVEX SETS BY
HYPERPLANES 462 G.2.4 THE EXTERNAL CHARACTERIZATION OF ALGEBRAICALLY
CLOSED AND CONVEX SETS 471 G.2.5 SUPPORTING HYPERPLANES 473 G.2.6*
SUPERLINEAR MAPS 476 G.3 REFLECTIONS ON W 480 G.3.1 SEPARATION IN R 480
G.3.2 SUPPORT IN R N 486 G.3.3 THE CAUCHY-SCHWARZ INEQUALITY 488 G.3.4
BEST APPROXIMATION FROM A CONVEX SET IN R N 489 G.3.5 ORTHOGONAL
COMPLEMENTS 492 G.3.6 EXTENSION OF POSITIVE LINEAR FUNCTIONALS,
REVISITED 496 CONTENTS I XIN CHAPTER H ECONOMIC APPLICATIONS 498 H.I
APPLICATIONS TO EXPECTED UTILITY THEORY 499 H.I.I THE EXPECTED
MULTI-UTILITY THEOREM 499 H.1.2* KNIGHTIAN UNCERTAINTY 505 H.I.3* THE
GILBOA-SCHMEIDLER MULTI-PRIOR MODEL 509 H.2 APPLICATIONS TO WELFARE
ECONOMICS 521 H.2.1 THE SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS
521 H.2.2 CHARACTERIZATION OF PARETO OPTIMA 525 H.2.3* HARSANYI S
UTILITARIANISM THEOREM 526 H.3 AN APPLICATION TO INFORMATION THEORY 528
H.4 APPLICATIONS TO FINANCIAL ECONOMICS 535 H.4.1 VIABILITY AND
ARBITRAGE-FREE PRICE FUNCTIONALS 535 H.4.2 THE NO-ARBITRAGE THEOREM 539
H.5 APPLICATIONS TO COOPERATIVE GAMES 542 H.5.1 THE NASH BARGAINING
SOLUTION 542 H.5.2* COALITIONAL GAMES WITHOUT SIDE PAYMENTS 546 PART IV
ANALYSIS ON METRIC/NORMED LINEAR SPACES 551 CHAPTER I METRIC LINEAR
SPACES 553 1.1 METRIC LINEAR SPACES 554 1.2 CONTINUOUS LINEAR OPERATORS
AND FUNCTIONALS 561 1.2.1 EXAMPLES OF (DIS-)CONTINUOUS LINEAR OPERATORS
561 1.2.2 CONTINUITY OF POSITIVE LINEAR FUNCTIONALS 567 1.2.3 CLOSED
VERSUS DENSE HYPERPLANES 569 1.2.4 DIGRESSION: ON THE CONTINUITY OF
CONCAVE FUNCTIONS 573 1.3 FINITE-DIMENSIONAL METRIC LINEAR SPACES 577
1.4* COMPACT SETS IN METRIC LINEAR SPACES 582 XIV I CONTENTS 1.5 CONVEX
ANALYSIS IN METRIC LINEAR SPACES 587 1.5.1 CLOSURE AND INTERIOR OF A
CONVEX SET 587 1.5.2 INTERIOR VERSUS ALGEBRAIC INTERIOR OF A CONVEX SET
590 1.5.3 EXTENSION OF POSITIVE LINEAR FUNCTIONALS, REVISITED 594 1.5.4
SEPARATION BY CLOSED HYPERPLANES 594 1.5.5* INTERIOR VERSUS ALGEBRAIC
INTERIOR OF A CLOSEDAND CONVEX SET 597 CHAPTER J NORMED LINEAR SPACES
601 J.I NORMED LINEAR SPACES 602 J.I.I A GEOMETRIC MOTIVATION 602 J.I.2
NORMED LINEAR SPACES 605 J.I.3 EXAMPLES OF NORMED LINEAR SPACES 607
J.I.4 METRIC VERSUS NORMED LINEAR SPACES 611 J.I.5 DIGRESSION: THE
LIPSCHITZ CONTINUITY OF CONCAVE MAPS 614 J.2 BANACH SPACES 616 J.2.1
DEFINITION AND EXAMPLES 616 J.2.2 INFINITE SERIES IN BANACH SPACES 618
J.2.3* ON THE SIZE OF BANACH SPACES 620 J.3 FIXED POINT THEORY IV 623
J.3.1 THE GLICKSBERG-FAN FIXED POINT THEOREM 623 J.3.2 APPLICATION:
EXISTENCE OF THE NASH EQUILIBRIUM, REVISITED 625 J.3.3* THE SCHAUDER
FIXED POINT THEOREMS 626 J.3.4* SOME CONSEQUENCES OF SCHAUDER S THEOREMS
630 J.3.5* APPLICATIONS TO FUNCTIONAL EQUATIONS 634 J.4 BOUNDED LINEAR
OPERATORS AND FUNCTIONALS 638 J.4.1 DEFINITIONS AND EXAMPLES 638 J.4.2
LINEAR HOMEOMORPHISMS, REVISITED 642 J.4.3 THE OPERATOR NORM 644 J.4.4
DUAL SPACES 648 J.4.5* DISCONTINUOUS LINEAR FUNCTIONALS, REVISITED 649
CONTENTS | XV J.5 CONVEX ANALYSIS IN NORMED LINEAR SPACES 650 J.5.1
SEPARATION BY CLOSED HYPERPLANES, REVISITED 650 J.5.2* BEST
APPROXIMATION FROM A CONVEX SET 652 J.5.3 EXTREME POINTS 654 J.6
EXTENSION IN NORMED LINEAR SPACES 661 J.6.1 EXTENSION OF CONTINUOUS
LINEAR FUNCTIONALS 661 J.6.2* INFINITE-DIMENSIONAL NORMED LINEAR SPACES
663 J.7* THE UNIFORM BOUNDEDNESS PRINCIPLE 665 CHAPTER K DIFFERENTIAL
CALCULUS 670 K.1 FRECHET DIFFERENTIATION 671 K.I.I LIMITS OF FUNCTIONS
AND TANGENCY 671 K.I.2 WHAT IS A DERIVATIVE? 672 K.I.3 THE FRECHET
DERIVATIVE 675 K.1.4 EXAMPLES 679 K.I.5 RULES OF DIFFERENTIATION 686
K.1.6 THE SECOND FRECHET DERIVATIVE OF A REAL FUNCTION 690 K.1.7
DIFFERENTIATION ON RELATIVELY OPEN SETS 694 K.2 GENERALIZATIONS OF THE
MEAN VALUE THEOREM 698 K.2.1 THE GENERALIZED MEAN VALUE THEOREM 698
K.2.2* THE MEAN VALUE INEQUALITY 701 K.3 FRECHET DIFFERENTIATION AND
CONCAVE MAPS 704 K.3.1 REMARKS ON THE DIFFERENTIABILITY OF CONCAVE MAPS
704 K.3.2 FRECHET DIFFERENTIABLE CONCAVE MAPS 706 K.4 OPTIMIZATION 712
K.4.1 LOCAL EXTREMA OF REAL MAPS 712 K.4.2 OPTIMIZATION OF CONCAVE MAPS
716 K.5 CALCULUS OF VARIATIONS 718 K.5.1 FINITE-HORIZON VARIATIONAL
PROBLEMS 718 K.5.2 THE EULER-LAGRANGE EQUATION 721 K.5.3* MORE ON THE
SUFFICIENCY OF THE EULER-LAGRANGE EQUATION 733 K.5.4 INFINITE-HORIZON
VARIATIONAL PROBLEMS 736 XVI I CONTENTS K.5.5 APPLICATION: THE OPTIMAL
INVESTMENT PROBLEM 738 K.5.6 APPLICATION: THE OPTIMAL GROWTH PROBLEM 740
K.5.7* APPLICATION: THE POINCARE-WIRTINGER INEQUALITY 743 HINTS FOR
SELECTED EXERCISES 747 REFERENCES 777 GLOSSARY OF SELECTED SYMBOLS 789
INDEX 793
|
| adam_txt |
REAL ANALYSIS WITH ECONOMIC APPLICATIONS EFE A. OK PRINCETON UNIVERSITY
PRESS I PRINCETON AND OXFORD CONTENTS PREFACE XVII PREREQUISITES XXVII
BASIC CONVENTIONS XXIX PART I SET THEORY 1 CHAPTER A PRELIMINARIES OF
REAL ANALYSIS 3 A.I ELEMENTS OF SET THEORY 4 A.I.I SETS 4 A. 1.2
RELATIONS 9 A. 1.3 EQUIVALENCE RELATIONS 11 A.1.4 ORDER RELATIONS 14 A.
1.5 FUNCTIONS 20 A.1.6 SEQUENCES, VECTORS, AND MATRICES 27 A.1.7* A
GLIMPSE OF ADVANCED SET THEORY: THE AXIOM OF CHOICE 29 A.2 REAL NUMBERS
33 A.2.1 ORDERED FIELDS 33 A.2.2 NATURAL NUMBERS, INTEGERS, AND
RATIONALS 37 A.2.3 REAL NUMBERS 39 A.2.4 INTERVALS AND 1 44 A. 3 REAL
SEQUENCES 46 A.3.1 CONVERGENT SEQUENCES 46 A.3.2 MONOTONIC SEQUENCES 50
A.3.3 SUBSEQUENTIAL LIMITS 53 VIN I CONTENTS A.3.4 INFINITE SERIES 56
A.3.5 REARRANGEMENT OF INFINITE SERIES 59 A.3.6 INFINITE PRODUCTS 61 A.4
REAL FUNCTIONS 62 A.4.1 BASIC DEFINITIONS 62 A.4.2 LIMITS, CONTINUITY,
AND DIFFERENTIATION 64 A.4.3 RIEMANN INTEGRATION 69 A.4.4 EXPONENTIAL,
LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS 74 A.4.5 CONCAVE AND CONVEX
FUNCTIONS 77 A.4.6 QUASICONCAVE AND QUASICONVEX FUNCTIONS 80 CHAPTER B
COUNTABILITY 82 B.I COUNTABLE AND UNCOUNTABLE SETS 82 B.2 LOSETSANDQ 90
B.3 SOME MORE ADVANCED SET THEORY 93 B.3.1 THE CARDINALITY ORDERING 93
B.3.2* THE WELL-ORDERING PRINCIPLE 98 B.4 APPLICATION: ORDINAL UTILITY
THEORY 99 B.4.1 PREFERENCE RELATIONS 100 B.4.2 UTILITY REPRESENTATION OF
COMPLETE PREFERENCE RELATIONS 102 B.4.3* UTILITY REPRESENTATION OF
INCOMPLETE PREFERENCE RELATIONS 107 PART II ANALYSIS ON METRIC SPACES
115 CHAPTER C METRIC SPACES 117 C.I BASIC NOTIONS 118 C.I.I METRIC
SPACES: DEFINITION AND EXAMPLES 119 C.1.2 OPEN AND CLOSED SETS 127 C.I.3
CONVERGENT SEQUENCES 132 CONTENTS I IX C.1.4 SEQUENTIAL CHARACTERIZATION
OF CLOSED SETS 134 C.I.5 EQUIVALENCE OF METRICS 136 C.2 CONNECTEDNESS
AND SEPARABILITY 138 C.2.1 CONNECTED METRIC SPACES 138 C.2.2 SEPARABLE
METRIC SPACES 140 C.2.3 APPLICATIONS TO UTILITY THEORY 145 C.3
COMPACTNESS 147 C.3.1 BASIC DEFINITIONS AND THE HEINE-BOREL THEOREM 148
C.3.2 COMPACTNESS AS A FINITE STRUCTURE 151 C.3.3 CLOSED AND BOUNDED
SETS 154 C.4 SEQUENTIAL COMPACTNESS 157 C.5 COMPLETENESS 161 C.5.1
CAUCHY SEQUENCES 161 C.5.2 COMPLETE METRIC SPACES: DEFINITION AND
EXAMPLES 163 C.5.3 COMPLETENESS VERSUS CLOSEDNESS 167 C.5.4 COMPLETENESS
VERSUS COMPACTNESS 171 C.6 FIXED POINT THEORY I 172 C.6.1 CONTRACTIONS
172 C.6.2 THE BANACH FIXED POINT THEOREM 175 C.6.3* GENERALIZATIONS OF
THE BANACH FIXED POINT THEOREM 179 C.7 APPLICATIONS TO FUNCTIONAL
EQUATIONS 183 C.7.1 SOLUTIONS OF FUNCTIONAL EQUATIONS 183 C.7.2 PICARD'S
EXISTENCE THEOREMS 187 C.8 PRODUCTS OF METRIC SPACES 192 C.8.1 FINITE
PRODUCTS 192 C.8.2 COUNTABLY INFINITE PRODUCTS 193 CHAPTER D CONTINUITY
I 200 D.I CONTINUITY OF FUNCTIONS 201 D.I.I DEFINITIONS AND EXAMPLES 201
D.I.2 UNIFORM CONTINUITY 208 X I CONTENTS D.I.3 OTHER CONTINUITY
CONCEPTS 210 D.I.4* REMARKS ON THE DIFFERENTIABILITY OF REAL FUNCTIONS
212 D.I.5 A FUNDAMENTAL CHARACTERIZATION OF CONTINUITY 213 D.I.6
HOMEOMORPHISMS 216 D.2 CONTINUITY AND CONNECTEDNESS 218 D.3 CONTINUITY
AND COMPACTNESS 222 D.3.1 CONTINUOUS IMAGE OF A COMPACT SET 222 D.3.2
THE LOCAL-TO-GLOBAL METHOD 223 D.3.3 WEIERSTRASS' THEOREM 225 D.4
SEMICONTINUITY 229 D.5 APPLICATIONS 237 D.5.1* CARISTI'S FIXED POINT
THEOREM 238 D.5.2 CONTINUOUS REPRESENTATION OF A PREFERENCE RELATION 239
D.5.3* CAUCHY'S FUNCTIONAL EQUATIONS: ADDITIVITY ON R" 242 D.5.4*
REPRESENTATION OF ADDITIVE PREFERENCES 247 D.6 CB(T) AND UNIFORM
CONVERGENCE 249 D.6.1 THE BASIC METRIC STRUCTURE OF CB(T) 249 D.6.2
UNIFORM CONVERGENCE 250 D.6.3* THE STONE-WEIERSTRASS THEOREM AND
SEPARABILITY OF C(T) 257 D.6.4* THE ARZELA-ASCOLI THEOREM 262
D.7*EXTENSION OF CONTINUOUS FUNCTIONS 266 D.8 FIXED POINT THEORY II 272
D.8.1 THE FIXED POINT PROPERTY 273 D.8.2 RETRACTS 274 D.8.3 THE BROUWER
FIXED POINT THEOREM 277 D.8.4 APPLICATIONS 280 S CHAPTER E CONTINUITY II
283 E.I CORRESPONDENCES 284 E.2 CONTINUITY OF CORRESPONDENCES 287 E.2.1
UPPER HEMICONTINUITY 287 E.2.2 THE CLOSED GRAPH PROPERTY 294 E.2.3 LOWER
HEMICONTINUITY 297 CONTENTS I XI E.2.4 CONTINUOUS CORRESPONDENCES 300
E.2.5* THE HAUSDORFF METRIC AND CONTINUITY 302 E.3 THE MAXIMUM THEOREM
306 E.4 APPLICATION: STATIONARY DYNAMIC PROGRAMMING 311 E.4.1 THE
STANDARD DYNAMIC PROGRAMMING PROBLEM 312 E.4.2 THE PRINCIPLE OF
OPTIMALITY 315 E.4.3 EXISTENCE AND UNIQUENESS OF AN OPTIMAL SOLUTION 320
E.4.4 APPLICATION: THE OPTIMAL GROWTH MODEL 324 E.5 FIXED POINT THEORY
III 330 E.5.1 KAKUTANI'S FIXED POINT THEOREM 331 E.5.2* MICHAEL'S
SELECTION THEOREM 333 E.5.3* PROOF OF KAKUTANI'S FIXED POINT THEOREM 339
E.5.4* CONTRACTIVE CORRESPONDENCES 341 E.6 APPLICATION: THE NASH
EQUILIBRIUM 343 E.6.1 STRATEGIC GAMES 343 E.6.2 THE NASH EQUILIBRIUM 346
E.6.3* REMARKS ON THE EQUILIBRIA OF DISCONTINUOUS GAMES 351 PART III
ANALYSIS ON LINEAR SPACES 355 CHAPTER F LINEAR SPACES 357 F.I LINEAR
SPACES 358 F.I.I ABELIAN GROUPS 358 F.I.2 LINEAR SPACES: DEFINITION AND
EXAMPLES 360 F.I.3 LINEAR.SUBSPACES, AFFINE MANIFOLDS, AND HYPERPLANES
364 F.1.4 SPAN AND AFFINE HULL OF A SET 368 F.I.5 LINEAR AND AFFINE
INDEPENDENCE 370 F.I.6 BASES AND DIMENSION 375 F.2 LINEAR OPERATORS AND
FUNCTIONALS 382 F.2.1 DEFINITIONS AND EXAMPLES 382 F.2.2 LINEAR AND
AFFINE FUNCTIONS 386 XII I CONTENTS F.2.3 LINEAR ISOMORPHISMS 389 F.2.4
HYPERPLANES, REVISITED 392 F.3 APPLICATION: EXPECTED UTILITY THEORY 395
F.3.1 THE EXPECTED UTILITY THEOREM 395 F.3.2 UTILITY THEORY UNDER
UNCERTAINTY 403 F.4* APPLICATION: CAPACITIES AND THE SHAPLEY VALUE 409
F.4.1 CAPACITIES AND COALITIONAL GAMES 410 F.4.2 THE LINEAR SPACE OF
CAPACITIES 412 F.4.3 THE SHAPLEY VALUE 415 CHAPTER G CONVEXITY 422 G.I
CONVEX SETS 423 G.I.I BASIC DEFINITIONS AND EXAMPLES 423 G.1.2 CONVEX
CONES 428 G.I.3 ORDERED LINEAR SPACES 432 G.1.4 ALGEBRAIC AND RELATIVE
INTERIOR OF A SET 436 G.1.5 ALGEBRAIC CLOSURE OF A SET 447 G.I.6
FINITELY GENERATED CONES 450 G.2 SEPARATION AND EXTENSION IN LINEAR
SPACES 454 G.2.1 EXTENSION OF LINEAR FUNCTIONALS 455 G.2.2 EXTENSION OF
POSITIVE LINEAR FUNCTIONALS 460 G.2.3 SEPARATION OF CONVEX SETS BY
HYPERPLANES 462 G.2.4 THE EXTERNAL CHARACTERIZATION OF ALGEBRAICALLY
CLOSED AND CONVEX SETS 471 G.2.5 SUPPORTING HYPERPLANES 473 G.2.6*
SUPERLINEAR MAPS 476 G.3 REFLECTIONS ON W 480 G.3.1 SEPARATION IN R" 480
G.3.2 SUPPORT IN R N 486 G.3.3 THE CAUCHY-SCHWARZ INEQUALITY 488 G.3.4
BEST APPROXIMATION FROM A CONVEX SET IN R N 489 G.3.5 ORTHOGONAL
COMPLEMENTS 492 G.3.6 EXTENSION OF POSITIVE LINEAR FUNCTIONALS,
REVISITED 496 CONTENTS I XIN CHAPTER H ECONOMIC APPLICATIONS 498 H.I
APPLICATIONS TO EXPECTED UTILITY THEORY 499 H.I.I THE EXPECTED
MULTI-UTILITY THEOREM 499 H.1.2* KNIGHTIAN UNCERTAINTY 505 H.I.3* THE
GILBOA-SCHMEIDLER MULTI-PRIOR MODEL 509 H.2 APPLICATIONS TO WELFARE
ECONOMICS 521 H.2.1 THE SECOND FUNDAMENTAL THEOREM OF WELFARE ECONOMICS
521 H.2.2 CHARACTERIZATION OF PARETO OPTIMA 525 H.2.3* HARSANYI'S
UTILITARIANISM THEOREM 526 H.3 AN APPLICATION TO INFORMATION THEORY 528
H.4 APPLICATIONS TO FINANCIAL ECONOMICS 535 H.4.1 VIABILITY AND
ARBITRAGE-FREE PRICE FUNCTIONALS 535 H.4.2 THE NO-ARBITRAGE THEOREM 539
H.5 APPLICATIONS TO COOPERATIVE GAMES 542 H.5.1 THE NASH BARGAINING
SOLUTION 542 H.5.2* COALITIONAL GAMES WITHOUT SIDE PAYMENTS 546 PART IV
ANALYSIS ON METRIC/NORMED LINEAR SPACES 551 CHAPTER I METRIC LINEAR
SPACES 553 1.1 METRIC LINEAR SPACES 554 1.2 CONTINUOUS LINEAR OPERATORS
AND FUNCTIONALS 561 1.2.1 EXAMPLES OF (DIS-)CONTINUOUS LINEAR OPERATORS
561 1.2.2 CONTINUITY OF POSITIVE LINEAR FUNCTIONALS 567 1.2.3 CLOSED
VERSUS DENSE HYPERPLANES 569 1.2.4 DIGRESSION: ON THE CONTINUITY OF
CONCAVE FUNCTIONS 573 1.3 FINITE-DIMENSIONAL METRIC LINEAR SPACES 577
1.4* COMPACT SETS IN METRIC LINEAR SPACES 582 XIV I CONTENTS 1.5 CONVEX
ANALYSIS IN METRIC LINEAR SPACES 587 1.5.1 CLOSURE AND INTERIOR OF A
CONVEX SET 587 1.5.2 INTERIOR VERSUS ALGEBRAIC INTERIOR OF A CONVEX SET
590 1.5.3 EXTENSION OF POSITIVE LINEAR FUNCTIONALS, REVISITED 594 1.5.4
SEPARATION BY CLOSED HYPERPLANES 594 1.5.5* INTERIOR VERSUS ALGEBRAIC
INTERIOR OF A CLOSEDAND CONVEX SET 597 CHAPTER J NORMED LINEAR SPACES
601 J.I NORMED LINEAR SPACES 602 J.I.I A GEOMETRIC MOTIVATION 602 J.I.2
NORMED LINEAR SPACES 605 J.I.3 EXAMPLES OF NORMED LINEAR SPACES 607
J.I.4 METRIC VERSUS NORMED LINEAR SPACES 611 J.I.5 DIGRESSION: THE
LIPSCHITZ CONTINUITY OF CONCAVE MAPS 614 J.2 BANACH SPACES 616 J.2.1
DEFINITION AND EXAMPLES 616 J.2.2 INFINITE SERIES IN BANACH SPACES 618
J.2.3* ON THE "SIZE" OF BANACH SPACES 620 J.3 FIXED POINT THEORY IV 623
J.3.1 THE GLICKSBERG-FAN FIXED POINT THEOREM 623 J.3.2 APPLICATION:
EXISTENCE OF THE NASH EQUILIBRIUM, REVISITED 625 J.3.3* THE SCHAUDER
FIXED POINT THEOREMS 626 J.3.4* SOME CONSEQUENCES OF SCHAUDER'S THEOREMS
630 J.3.5* APPLICATIONS TO FUNCTIONAL EQUATIONS 634 J.4 BOUNDED LINEAR
OPERATORS AND FUNCTIONALS 638 J.4.1 DEFINITIONS AND EXAMPLES 638 J.4.2
LINEAR HOMEOMORPHISMS, REVISITED 642 J.4.3 THE OPERATOR NORM 644 J.4.4
DUAL SPACES 648 J.4.5* DISCONTINUOUS LINEAR FUNCTIONALS, REVISITED 649
CONTENTS | XV J.5 CONVEX ANALYSIS IN NORMED LINEAR SPACES 650 J.5.1
SEPARATION BY CLOSED HYPERPLANES, REVISITED 650 J.5.2* BEST
APPROXIMATION FROM A CONVEX SET 652 J.5.3 EXTREME POINTS 654 J.6
EXTENSION IN NORMED LINEAR SPACES 661 J.6.1 EXTENSION OF CONTINUOUS
LINEAR FUNCTIONALS 661 J.6.2* INFINITE-DIMENSIONAL NORMED LINEAR SPACES
663 J.7* THE UNIFORM BOUNDEDNESS PRINCIPLE 665 CHAPTER K DIFFERENTIAL
CALCULUS 670 K.1 FRECHET DIFFERENTIATION 671 K.I.I LIMITS OF FUNCTIONS
AND TANGENCY 671 K.I.2 WHAT IS A DERIVATIVE? 672 K.I.3 THE FRECHET
DERIVATIVE 675 K.1.4 EXAMPLES 679 K.I.5 RULES OF DIFFERENTIATION 686
K.1.6 THE SECOND FRECHET DERIVATIVE OF A REAL FUNCTION 690 K.1.7
DIFFERENTIATION ON RELATIVELY OPEN SETS 694 K.2 GENERALIZATIONS OF THE
MEAN VALUE THEOREM 698 K.2.1 THE GENERALIZED MEAN VALUE THEOREM 698
K.2.2* THE MEAN VALUE INEQUALITY 701 K.3 FRECHET DIFFERENTIATION AND
CONCAVE MAPS 704 K.3.1 REMARKS ON THE DIFFERENTIABILITY OF CONCAVE MAPS
704 K.3.2 FRECHET DIFFERENTIABLE CONCAVE MAPS 706 K.4 OPTIMIZATION 712
K.4.1 LOCAL EXTREMA OF REAL MAPS 712 K.4.2 OPTIMIZATION OF CONCAVE MAPS
716 K.5 CALCULUS OF VARIATIONS 718 K.5.1 FINITE-HORIZON VARIATIONAL
PROBLEMS 718 K.5.2 THE EULER-LAGRANGE EQUATION 721 K.5.3* MORE ON THE
SUFFICIENCY OF THE EULER-LAGRANGE EQUATION 733 K.5.4 INFINITE-HORIZON
VARIATIONAL PROBLEMS 736 XVI I CONTENTS K.5.5 APPLICATION: THE OPTIMAL
INVESTMENT PROBLEM 738 K.5.6 APPLICATION: THE OPTIMAL GROWTH PROBLEM 740
K.5.7* APPLICATION: THE POINCARE-WIRTINGER INEQUALITY 743 HINTS FOR
SELECTED EXERCISES 747 REFERENCES 777 GLOSSARY OF SELECTED SYMBOLS 789
INDEX 793 |
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| callnumber-first | H - Social Science |
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| callnumber-subject | HB - Economic Theory and Demography |
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| dewey-full | 330.01/519 330.1/51 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.01/519 330.1/51 |
| dewey-search | 330.01/519 330.1/51 |
| dewey-sort | 3330.01 3519 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV022413114 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:22:49Z |
| indexdate | 2024-07-09T20:57:03Z |
| institution | BVB |
| isbn | 0691117683 9780691117683 |
| language | English |
| lccn | 2006049378 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015621569 |
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| physical | XXX, 802 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Ok, Efe A. Verfasser (DE-588)171401115 aut Real analysis with economic applications Efe A. Ok Princeton [u.a.] Princeton Univ. Press 2007 XXX, 802 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse (wiskunde) gtt Analyse mathématique Análise matemática larpcal Matemática aplicada (economia) larpcal Mathématiques économiques Wiskundige economie gtt Economics, Mathematical Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Reelle Analysis (DE-588)4627581-2 s DE-604 http://www.loc.gov/catdir/enhancements/fy0661/2006049378-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0708/2006049378-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015621569&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ok, Efe A. Real analysis with economic applications Analyse (wiskunde) gtt Analyse mathématique Análise matemática larpcal Matemática aplicada (economia) larpcal Mathématiques économiques Wiskundige economie gtt Economics, Mathematical Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 (DE-588)4151278-9 |
| title | Real analysis with economic applications |
| title_auth | Real analysis with economic applications |
| title_exact_search | Real analysis with economic applications |
| title_exact_search_txtP | Real analysis with economic applications |
| title_full | Real analysis with economic applications Efe A. Ok |
| title_fullStr | Real analysis with economic applications Efe A. Ok |
| title_full_unstemmed | Real analysis with economic applications Efe A. Ok |
| title_short | Real analysis with economic applications |
| title_sort | real analysis with economic applications |
| topic | Analyse (wiskunde) gtt Analyse mathématique Análise matemática larpcal Matemática aplicada (economia) larpcal Mathématiques économiques Wiskundige economie gtt Economics, Mathematical Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Analyse (wiskunde) Analyse mathématique Análise matemática Matemática aplicada (economia) Mathématiques économiques Wiskundige economie Economics, Mathematical Mathematical analysis Reelle Analysis Einführung |
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