An introduction to mathematical analysis for economic theory and econometrics:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2009
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017086387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXI, 671 S. graph. Darst. |
| ISBN: | 9780691118673 |
Internformat
MARC
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| 100 | 1 | |a Corbae, Dean |d 1960- |e Verfasser |0 (DE-588)132750163 |4 aut | |
| 245 | 1 | 0 | |a An introduction to mathematical analysis for economic theory and econometrics |c Dean Corbae ; Maxwell B. Stinchcombe ; Juraj Zeman |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a XXI, 671 S. |b graph. Darst. | ||
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| 650 | 4 | |a Mathematical analysis | |
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Datensatz im Suchindex
| _version_ | 1819269689949290496 |
|---|---|
| adam_text | Contents
Preface
xi
User s Guide
xiii
Notation
xix
Chapter
1 ♦
Logic
1
1.1
Statements, Sets, Subsets, and Implication
1
1.2
Statements and Their Truth Values
3
1.3
Proofs, a First Look
6
1.4
Logical Quantifiers
9
1.5
Taxonomy of Proofs
11
Chapter
2 ♦
Set Theory
15
2.1
Some Simple Questions
16
2.2
Notation and Other Basics
17
2.3
Products, Relations, Correspondences, and Functions
21
2.4
Equivalence Relations
26
2.5
Optimal Choice for Finite Sets
28
2.6
Direct and Inverse Images, Compositions
33
2.7
Weak and Partial Orders, Lattices
39
2.8
Monotonie
Changes in Optima: Supermodularity and Lattices
42
2.9
Tarski s Lattice Fixed-Point Theorem and Stable Matchings
49
2.10
Finite and Infinite Sets
56
2.11
The Axiom of Choice and Some Equivalent Results
62
2.12
Revealed Preference and Rationalizability
64
2.13
Superstructures
68
2.14
Bibliography
69
2.15
End-of-Chapter Problems
70
Chapter
3 ♦
The Space of Real Numbers
72
3.1
Why We Want More Than the Rationals
72
3.2
Basic Properties of Rationals
73
3.3
Distance, Cauchy Sequences, and the Real Numbers
75
vii
viii
♦ Contents
3.4
The Completeness of the Real Numbers
3.5
Examples Using Completeness
3.6
Supremum and Infimum
3.7
Summability
3.8
Products of Sequences and ex
3.9
Patience,
Lim inf,
and
Lim sup
3.10
Some Perspective on Completing the Rationals
3.11
Bibliography
82
87
90
92
99
101
104
105
Chapter
4 ♦
The Finite-Dimensional Metric Space
of Real Vectors
106
4.1
The Basic Definitions for Metric Spaces
107
4.2
Discrete Spaces
113
4.3
Шг
as a Normed Vector Space
114
4.4
Completeness
120
4.5
Closure, Convergence, and Completeness
124
4.6
Separability
128
4.7
Compactness in R£
129
4.8
Continuous Functions on Re
136
4.9
Lipschitz and Uniform Continuity
143
4.10
Correspondences and the Theorem of the Maximum
144
4.11
Banach s Contraction Mapping Theorem
154
4.12
Connectedness
167
4.13
Bibliography
171
Chapter
5 ♦
Finite-Dimensional Convex Analysis
172
5.1
The Basic Geometry of Convexity
173
5.2
The Dual Space of Re
181
5.3
The Three Degrees of Convex Separation
184
5.4
Strong Separation and Neoclassical Duality
186
5.5
Boundary Issues
194
5.6
Concave and Convex Functions
199
5.7
Separation and the Hahn-Banach Theorem
209
5.8
Separation and the Kuhn-Tucker Theorem
214
5.9
Interpreting
Lagrange
Multipliers
228
5.10
Differentiability and Concavity
232
5.11
Fixed-Point Theorems and General Equilibrium Theory
239
5.12
Fixed-Point Theorems for Nash Equilibria and Perfect Equilibria
245
5.13
Bibliography
258
Chapter
6 ♦
Metric Spaces
259
6.1
The Space of Compact Sets and the Theorem of the Maximum
260
6.2
Spaces of Continuous Functions
272
6.3
ľ(K),
the Space of Cumulative Distribution Functions
293
6.4
Approximation in C(M) when
M
Is Compact
297
6.5
Regression Analysis as Approximation Theory
304
6.6
Countable Product Spaces and Sequence Spaces
311
Contents ♦ ix
6.7
Defining Functions Implicitly and by
Extension
321
6.8
The Metric Completion Theorem
331
6.9
The Lebesgue Measure Space
335
6.10
Bibliography
343
6.11
End-of-Chapter Problems
344
Chapter
7 ♦
Measure Spaces and Probability
355
7.1
The Basics of Measure Theory
356
7.2
Four Limit Results
370
7.3
Good Sets Arguments and Measurability
388
7.4
Two
0-1
Laws
397
7.5
Dominated Convergence, Uniform Integrability,
and Continuity of the Integral
400
7.6
The Existence of Nonatomic Countably Additive Probabilities
411
7.7
Transition Probabilities, Product Measures,
and Fubini s Theorem
423
7.8
Seriously Nonmeasurable Sets and Intergenerational Equity
426
7.9
Null Sets, Completions of
σ
-Fields, and Measurable Optima
430
7.10
Convergence in Distribution and Skorohod s Theorem
436
7.11
Complements and Extras
440
7.12
Appendix on Lebesgue Integration
448
7.13
Bibliography
451
Chapter
8 ♦
The Lp{u,
3,
P) and lp Spaces,
ρ
Є
[1,
σο]
452
8.1
Some Uses in Statistics and Econometrics
453
8.2
Some Uses in Economic Theory
456
8.3
The Basics of
¿Ρ(Ω,
Э ,
Ρ)
and
ЄР
458
8.4
Regression Analysis
474
8.5
Signed Measures, Vector Measures, and Densities
490
8.6
Measure Space Exchange Economies
498
8.7
Measure Space Games
503
8.8
Dual Spaces: Representations and Separation
509
8.9
Weak Convergence in
¿Ρ(Ω,
7,
Ρ), ρ
є
[1,
σο)
518
8.10
Optimization of Nonlinear Operators
522
8.11
A Simple Case of Parametric Estimation
528
8.12
Complements and Extras
541
8.13
Bibliography
550
Chapter
9 ♦
Probabilities on Metric Spaces
551
9.1
Choice under Uncertainty
551
9.2
Stochastic Processes
552
9.3
The Metric Space (ACM), p)
553
9.4
Two Useful Implications
562
9.5
Expected Utility Preferences
563
9.6
The Riesz Representation Theorem for
Δ(Μ), Μ
Compact
567
9.7
Polish Measure Spaces and Polish Metric Spaces
569
9.8
The Riesz Representation Theorem for Polish Metric Spaces
571
χ
♦ Contents
9.9
Compactness in
Δ (Μ)
574
9.10 An Operator
Proof of the Central Limit Theorem
578
9.11
Regular Conditional Probabilities
583
9.12
Conditional Probabilities from Maximization
589
9.13
Nonexistence of rep s
590
9.14
Bibliography
594
Chapter
10 ♦
Infinite-Dimensional Convex Analysis
595
10.1
Topological Spaces
595
10.2
Locally Convex Topological Vector Spaces
603
10.3
The Dual Space and Separation
606
10.4
Filterbases,
Filters, and
Ultrafilters
610
10.5
Bases,
Subbases,
Nets, and Convergence
612
10.6
Compactness
617
10.7
Compactness in Topological Vector Spaces
621
10.8
Fixed Points
624
10.9
Bibliography
626
Chapter
11 ♦
Expanded Spaces
627
11.1
The Basics of *R
628
11.2
Superstructures, Transfer, Spillover, and Saturation
632
11.3
Loeb Spaces
642
11.4
Saturation, Star-Finite Maximization Models,
and Compactification
649
11.5
The Existence of a Purely Finitely Additive
{0,
lJ-Valued
μ
652
11.6
Problems and Complements
653
11.7
Bibliography
654
Index
655
|
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| discipline | Wirtschaftswissenschaften |
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| id | DE-604.BV035281178 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:27:34Z |
| institution | BVB |
| isbn | 9780691118673 |
| language | English |
| lccn | 2008047711 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017086387 |
| oclc_num | 267056151 |
| open_access_boolean | |
| owner | DE-N2 DE-384 DE-703 DE-355 DE-BY-UBR DE-M382 DE-19 DE-BY-UBM DE-706 DE-2070s DE-11 DE-188 |
| owner_facet | DE-N2 DE-384 DE-703 DE-355 DE-BY-UBR DE-M382 DE-19 DE-BY-UBM DE-706 DE-2070s DE-11 DE-188 |
| physical | XXI, 671 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spellingShingle | Corbae, Dean 1960- Stinchcombe, Maxwell B. Zeman, Juraj An introduction to mathematical analysis for economic theory and econometrics Economics, Mathematical Mathematical analysis Econometrics Ökonometrie (DE-588)4132280-0 gnd Maßtheorie (DE-588)4074626-4 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4074626-4 (DE-588)4066472-7 (DE-588)4001865-9 |
| title | An introduction to mathematical analysis for economic theory and econometrics |
| title_auth | An introduction to mathematical analysis for economic theory and econometrics |
| title_exact_search | An introduction to mathematical analysis for economic theory and econometrics |
| title_full | An introduction to mathematical analysis for economic theory and econometrics Dean Corbae ; Maxwell B. Stinchcombe ; Juraj Zeman |
| title_fullStr | An introduction to mathematical analysis for economic theory and econometrics Dean Corbae ; Maxwell B. Stinchcombe ; Juraj Zeman |
| title_full_unstemmed | An introduction to mathematical analysis for economic theory and econometrics Dean Corbae ; Maxwell B. Stinchcombe ; Juraj Zeman |
| title_short | An introduction to mathematical analysis for economic theory and econometrics |
| title_sort | an introduction to mathematical analysis for economic theory and econometrics |
| topic | Economics, Mathematical Mathematical analysis Econometrics Ökonometrie (DE-588)4132280-0 gnd Maßtheorie (DE-588)4074626-4 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Economics, Mathematical Mathematical analysis Econometrics Ökonometrie Maßtheorie Wirtschaftsmathematik Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017086387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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