Infinite dimensional analysis: a hitchhiker's guide
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer-Verlag
[1994]
|
| Schriftenreihe: | Studies in economic theory
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xviii, 603 Seiten Diagramme |
| ISBN: | 3540583084 0387583084 |
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| 245 | 1 | 0 | |a Infinite dimensional analysis |b a hitchhiker's guide |c Charalambos D. Aliprantis ; Kim C. Border |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CHARALAMBOS D. ALIPRANTIS
YY
KIM C. BORDER
INFINITE
DIMENSIONAL
ANALYSIS
A
HITCHHIKER'S GUIDE
WITH
16
FIGURES
SPRINGER-VERLAG
BERLIN
HEIDELBERG NEW YORK
LONDON
PARIS TOKYO
HONG
KONG BARCELONA
BUDAPEST
CONTENTS
PREFACE VII
A FOREWORD TO THE PRACTICAL XV
1 ODDS AND ENDS 1
1.1 PREREQUISITES 1
1.2 SET THEORETIC NOTATION 2
1.3 INFINITES 3
1.4 NUMBERS 5
1.5 RELATIONS, CORRESPONDENCES, AND FUNCTIONS 6
1.6 DUALITY OF EVALUATION 8
1.7 A BESTIARY OF RELATIONS 8
1.8 EQUIVALENCE RELATIONS 10
1.9 ORDERS AND SUCH 11
1.10 THE AXIOM OF CHOICE AND AXIOMATIC SET THEORY 11
1.11 ZORN'S LEMMA 13
1.12 ORDINALS 17
2 TOPOLOGY 20
2.1 TOPOLOGICAL SPACES 22
2.2 NEIGHBORHOODS AND CLOSURES 25
2.3 DENSE SUBSETS 27
2.4 NETS 28
2.5 FILTERS 32
2.6 NETS AND FILTERS 35
2.7 CONTINUOUS FUNCTIONS 36
2.8 COMPACTNESS 38
2.9 NETS VS. SEQUENCES 42
2.10 SEMICONTINUOUS FUNCTIONS 43
2.11 SEPARATION PROPERTIES 45
2.12 COMPARING TOPOLOGIES 47
2.13 WEAK TOPOLOGIES 48
X
CONTENTS
2.14 THE PRODUCT TOPOLOGY 51
2.15 POINTWISE AND UNIFORM CONVERGENCE 54
2.16 LOCALLY COMPACT SPACES 56
2.17 THE STONE-CECH COMPACTIFICATION 59
2.18 STONE-CECH COMPACTIFICATION OF A DISCRETE SET 64
2.19 PARACOMPACT SPACES AND PARTITIONS OF UNITY 67
3 METRIZABLE SPACES 70
3.1 METRIE SPACES 71
3.2 EQUIVALENT METRICS AND COMPLETENESS 73
3.3 UNIFORMLY CONTINUOUS FUNCTIONS 75
3.4 UNIFORMITIES 77
3.5 DISTANCE FUNCTIONS 79
3.6 SEMICONTINUOUS FUNCTIONS 81
3.7 EMBEDDINGS AND COMPLETIONS 82
3.8 COMPACTNESS AND COMPLETENESS 83
3.9 THE BAIRE CATEGORY THEOREM 87
3.10 CONTRACTION MAPPINGS 88
3.11 COUNTABLE PRODUETS OF METRIC SPACES 89
3.12 THE HUBERT CUBE 91
3.13 LOCALLY COMPACT METRIZABLE SPACES 92
3.14 THE CANTOR SET 93
3.15 THE SPACE
D\T
OF NATURAL SEQUENCES 96
3.16 HAUSDORFF METRIC 99
3.17 TOPOLOGY OF CLOSED CONVERGENCE 106
3.18 THE SPACE
C(X,Y)
112
4
TOPOLOGICAL VECTOR
SPACES
116
4.1 LINEAR TOPOLOGIES 119
4.2 ABSORBING AND CIRCLED SETS 121
4.3 CONVEX SETS 125
4.4 CONVEX AND CONEAVE FUNCTIONS 129
4.5 CONVEX FUNCTIONS ON FINITE DIMENSIONAL SPACES 133
4.6 SUBLINEAR FUNCTIONS AND GAUGES 134
4.7 THE HAHN-BANACH EXTENSION THEOREM 138
4.8 SEPARATING HYPERPLANE THEOREMS 140
4.9 SEPARATION BY CONTINUOUS FUNCTIONALS 143
4.10 LOCALLY CONVEX SPACES AND SEMINORMS 144
4.11 SEPARATION IN LOCALLY CONVEX SPACES 147
4.12 FINITE DIMENSIONAL TOPOLOGICAL VECTOR SPACES 148
4.13 DUAL PAIRS 151
4.14 TOPOLOGIES CONSISTENT WITH A GIVEN DUAL 153
CONTENTS XI
4.15 POLARS 154
4.16 -TOPOLOGIES 161
4.17 THE MACKEY TOPOLOGY 163
4.18 MORE ABOUT SUPPORT FUNCTIONALS 166
4.19 THE STRONG TOPOLOGY 170
4.20 EXTREME POINTS 171
4.21 POLYTOPES AND WEAK NEIGHBORHOODS 176
5 NORMED SPACES 181
5.1 NORMED AND BANACH SPACES 183
5.2 LINEAR OPERATORS ON NORMED SPACES 184
5.3 THE NORM DUAL OF A NORMED SPACE 188
5.4 THE UNIFORM BOUNDEDNESS PRINCIPLE 190
5.5 WEAK TOPOLOGIES ON NORMED SPACES 193
5.6 METRIZABILITY OF WEAK TOPOLOGIES 196
5.7 SPACES OF CONVEX SETS 201
5.8 CONTINUITY OF THE EVALUATION 202
5.9 ADJOINT OPERATORS 204
6 RIESZ SPACES 206
6.1 ORDERS, LATTICES, AND CONES 207
6.2 RIESZ SPACES 208
6.3 ORDER BOUNDED SETS 210
6.4 ORDER AND LATTICE PROPERTIES 211
6.5 THE RIESZ DECOMPOSITION PROPERTY 215
6.6 DISJOINTNESS 215
6.7 RIESZ SUBSPACES AND IDEALS 216
6.8 ORDER CONVERGENCE AND ORDER CONTINUITY 217
6.9 BANDS 219
6.10 POSITIVE FUNCTIONALS 221
6.11 EXTENDING POSITIVE FUNCTIONALS 226
6.12 POSITIVE OPERATORS 228
6.13 TOPOLOGICAL RIESZ SPACES 230
6.14 THE BAND GENERATED BY
E'
235
6.15 RIESZ PAIRS 237
6.16 SYMMETRIE RIESZ PAIRS 240
7 BANACH LATTICES 244
7.1 FRECHET AND BANACH LATTICES 245
7.2 LATTICE HOMOMORPHISMS AND ISOMETRIES 249
7.3 ORDER CONTINUOUS NORMS 251
7.4 AM- AND AL-SPACES 253
XII CONTENTS
7.5 THE INTERIOR OF THE POSITIVE CONE 258
7.6 THE CURIOUS AL-SPACE
BV
0
260
7.7
THE STONE-WEIERSTRASS THEOREM 265
7.8 PROJECTIONS AND THE FIXED SPACE OF AN OPERATOR 266
8 CHARGES AND MEASURES 269
8.1 RINGS, SEMIRINGS, AND ALGEBRAS OF SETS 272
8.2 DYNKIN SYSTEMS 276
8.3 MEASURABLE FUNCTIONS 278
8.4 CHARGES AND MEASURES 281
8.5 OUTER MEASURES AND MEASURABLE SETS 285
8.6 THE CARATHEODORY EXTENSION OF A MEASURE 288
8.7 MEASURE SPACES 293
8.8 LEBESGUE MEASURE 295
8.9 PRODUCT MEASURES 298
8.10 MEASURES O
N
L
" 300
8.11 ATOMS 303
8.12 THE AL-SPACE OF CHARGES 304
8.13 THE AL-SPACE OF MEASURES 307
8.14 ABSOLUTE CONTINUITY 309
9 INTEGRALS 311
9.1 THE INTEGRAL OF A STEP FUNCTION 312
9.2 FINITELY ADDITIVE INTEGRATION OF BOUNDED FUNCTIONS 314
9.3 THE LEBESGUE INTEGRAL 316
9.4 THE BASIC PROPERTIES OF THE LEBESGUE INTEGRAL 321
9.5 THE EXTENDED LEBESGUE INTEGRAL 324
9.6 ITERATED INTEGRALS 326
9.7 THE RIEMANN INTEGRAL 328
9.8 THE BOCHNER INTEGRAL 331
9.9 THE GELFAND INTEGRAL 336
9.10 THE DUNFORD AND PETTIS INTEGRALS 339
10
LP-SPACES 341
10.1 LP-NORMS 342
10.2 INEQUALITIES OF HOLDER AND MINKOWSKI 343
10.3 DENSE SUBSPACES OF L
P
-SPACES
345
10.4
SUBLATTICES OF Z
P
-SPACES
346
10.5 SEPARABLE LI-SPACES AND MEASURES 347
10.6 THE RADON-NIKODYM THEOREM 350
10.7 EQUIVALENT MEASURES 351
10.8 DUALS OF LP-SPACES 353
CONTENTS
XIII
10.9 LYAPUNOV'S CONVEXITY THEOREM 355
10.10 CONVERGENCE IN MEASURE 359
10.11 CONVERGENCE IN MEASURE IN L
P
-SPACES
361
10.12
CHANGE OF VARIABLES 364
11 MEASURES AND TOPOLOGY 368
11.1 BOREL SETS AND BAIRE SETS 370
11.2 SPOTTING BOREL SETS 377
11.3 BOREL MEASURES AND REGULARITY 378
11.4 REGULAER BOREL MEASURES 382
11.5 THE SUPPORT OF A MEASURE 386
11.6 THE AM-SPACE
B
B
(E)
AND ITS DUAL 387
11.7
THE DUAL OF C(,(X) FOR NORMAL SPACES 391
11.8 THE DUAL OF
C
C
(X)
FOR LOCALLY COMPACT SPACES 396
11.9
BAIRE VS. BOREL MEASURES 399
11.10 HOMOMORPHISMS BETWEEN C(X)-SPACES 402
11.11 NONATOMIC BOREL MEASURES 405
11.12 ANALYTIC SETS 408
12 PROBABILITY MEASURES ON METRIZABLE SPACES 411
12.1 THE WEAK* TOPOLOGY ON
7 (X)
411
12.2 EMBEDDING
X
IN
7
(X) 417
12.3 PROPERTIES OF
7 (X)
419
12.4 THE MANY FACES OF
7 (X)
422
12.5 COMPACTNESS IN
7 (X)
423
12.6 INFINITE PRODUCTS OF PROBABILITY MEASURES 425
13 SPACES OF SEQUENCES 428
13.1 THE BASIC SEQUENCE SPACES 428
13.2 THE SEQUENCE SPACES R
N
AND
P
430
13.3 THE SEQUENCE SPACE
CQ
432
13.4 THE SEQUENCE SPACE C 434
13.5 THE P-SPACES 436
13.6
\
AND THE SYMMETRIE RIESZ PAIR (^OO ^I) 440
13.7 THE SEQUENCE SPACE 00 441
13.8 MORE ON 4
, =
BA(N)
447
13.9 EMBEDDING SEQUENCE SPACES 450
13.10 BANACH-MAZUR LIMITS AND INVARIANT MEASURES 454
13.11 SEQUENCES OF VECTOR SPACES 456
XIV CONTENTS
14 CORRESPONDENCES 458
14.1 BASIC DEFINITIONS 460
14.2 CONTINUITY OF CORRESPONDENCES 462
14.3 HEMICONTINUITY AND NETS 467
14.4 OPERATIONS ON CORRESPONDENCES 469
14.5 THE MAXIMUM THEOREM 472
14.6 VECTOR-VALUED CORRESPONDENCES 474
14.7 DEMICONTINUOUS CORRESPONDENCES 477
14.8 KNASTER-KURATOWSKI-MAZURKIEWICZ MAPPINGS 479
14.9 FIXED POINT THEOREMS 482
14.10 CONTRACTION CORRESPONDENCES 486
14.11 CONTINUOUS SELECTORS 487
14.12 MEASURABLE CORRESPONDENCES 491
14.13 CARATHEODORY FUNCTIONS 499
14.14 CORRESPONDENCES WITH MEASURABLE GRAPH 503
14.15 MEASURABLE SELECTORS 504
14.16 CORRESPONDENCES WITH COMPACT CONVEX VALUES 508
14.17 INTEGRATION OF CORRESPONDENCES 514
15 MARKOV TRANSITIONS 521
15.1 MARKOV AND STOCHASTIC OPERATORS 523
15.2 MARKOV TRANSITIONS AND KERNEIS 526
15.3 CONTINUOUS MARKOV TRANSITIONS 531
15.4 INVARIANT MEASURES 532
15.5 ERGODIC MEASURES 537
15.6 MARKOV TRANSITION CORRESPONDENCES 539
15.7 RANDOM FUNCTIONS 541
15.8 DILATIONS 546
15.9 MORE ON MARKOV OPERATORS 550
15.10 A NOTE ON "DYNAMICAL SYSTEMS" 553
16 ERGODICITY 554
16.1 MEASURE-PRESERVING TRANSFORMATIONS AND ERGODICITY 555
16.2
BIRKHOFF 'S ERGODIC THEOREM 558
16.3 ERGODIC OPERATORS 560
REFERENCES 567
INDEX 580 |
| any_adam_object | 1 |
| author | Aliprantis, Charalambos D. 1946-2009 Border, Kim C. 1952- |
| author_GND | (DE-588)121199010 (DE-588)121199037 |
| author_facet | Aliprantis, Charalambos D. 1946-2009 Border, Kim C. 1952- |
| author_role | aut aut |
| author_sort | Aliprantis, Charalambos D. 1946-2009 |
| author_variant | c d a cd cda k c b kc kcb |
| building | Verbundindex |
| bvnumber | BV009821005 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 150 SK 280 SK 600 |
| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)31011936 (DE-599)BVBBV009821005 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV009821005 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-07T11:07:06Z |
| institution | BVB |
| isbn | 3540583084 0387583084 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006502031 |
| oclc_num | 31011936 |
| open_access_boolean | |
| owner | DE-703 DE-12 DE-384 DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-824 DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-703 DE-12 DE-384 DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-824 DE-19 DE-BY-UBM DE-706 DE-83 DE-11 DE-188 |
| physical | xviii, 603 Seiten Diagramme |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Studies in economic theory |
| series2 | Studies in economic theory |
| spelling | Aliprantis, Charalambos D. 1946-2009 (DE-588)121199010 aut Infinite dimensional analysis a hitchhiker's guide Charalambos D. Aliprantis ; Kim C. Border Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer-Verlag [1994] © 1994 xviii, 603 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Studies in economic theory 4 Dimensieanalyse gtt Econometrie gtt Economics, Mathematical Functional analysis Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Analysis (DE-588)4001865-9 s Unendlichdimensionaler Raum (DE-588)4207852-0 s Wirtschaftsmathematik (DE-588)4066472-7 s 1\p DE-604 Border, Kim C. 1952- (DE-588)121199037 aut Erscheint auch als Online-Ausgabe 978-3-662-03004-2 Studies in economic theory 4 (DE-604)BV004683666 4 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006502031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aliprantis, Charalambos D. 1946-2009 Border, Kim C. 1952- Infinite dimensional analysis a hitchhiker's guide Studies in economic theory Dimensieanalyse gtt Econometrie gtt Economics, Mathematical Functional analysis Wirtschaftsmathematik (DE-588)4066472-7 gnd Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4207852-0 (DE-588)4018916-8 (DE-588)4001865-9 |
| title | Infinite dimensional analysis a hitchhiker's guide |
| title_auth | Infinite dimensional analysis a hitchhiker's guide |
| title_exact_search | Infinite dimensional analysis a hitchhiker's guide |
| title_full | Infinite dimensional analysis a hitchhiker's guide Charalambos D. Aliprantis ; Kim C. Border |
| title_fullStr | Infinite dimensional analysis a hitchhiker's guide Charalambos D. Aliprantis ; Kim C. Border |
| title_full_unstemmed | Infinite dimensional analysis a hitchhiker's guide Charalambos D. Aliprantis ; Kim C. Border |
| title_short | Infinite dimensional analysis |
| title_sort | infinite dimensional analysis a hitchhiker s guide |
| title_sub | a hitchhiker's guide |
| topic | Dimensieanalyse gtt Econometrie gtt Economics, Mathematical Functional analysis Wirtschaftsmathematik (DE-588)4066472-7 gnd Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Dimensieanalyse Econometrie Economics, Mathematical Functional analysis Wirtschaftsmathematik Unendlichdimensionaler Raum Funktionalanalysis Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006502031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004683666 |
| work_keys_str_mv | AT aliprantischaralambosd infinitedimensionalanalysisahitchhikersguide AT borderkimc infinitedimensionalanalysisahitchhikersguide |