Infinite dimensional analysis: a hitchhiker's guide
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York
Springer
[2006]
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| Edition: | third edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxii, 703 Seiten |
| ISBN: | 3540295860 9783540295860 9783540326960 |
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MARC
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| 245 | 1 | 0 | |a Infinite dimensional analysis |b a hitchhiker's guide |c Charalambos D. Aliprantis ; Kim C. Border |
| 250 | |a third edition | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York |b Springer |c [2006] | |
| 264 | 4 | |c © 2006 | |
| 300 | |a xxii, 703 Seiten | ||
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| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 7 | |a Funktionalanalysis |2 swd | |
| 650 | 7 | |a Mathématiques économiques |2 ram | |
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| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804135618903539712 |
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| adam_text | CHARALAMBOS D. ALIPRANTIS KIM C. BORDER INFINITE DIMENSIONAL ANALYSIS A
HITCHHIKER S GUIDE THIRD EDITION WITH 38 FIGURES AND 1 TABLE _J
SPRINGER CONTENTS PREFACE TO THE THIRD EDITION VII A FOREWORD TO THE
PRACTICAL XIX 1 ODDS AND ENDS 1 1.1 NUMBERS 1 1.2 SETS 2 1.3 RELATIONS,
CORRESPONDENCES, AND FUNCTIONS 4 1.4 A BESTIARY OF RELATIONS 5 1.5
EQUIVALENCE RELATIONS 7 1.6 ORDERS AND SUCH 7 1.7 REAL FUNCTIONS 8 1.8
DUALITY OF EVALUATION 9 1.9 INFINITIES 10 1.10 THE DIAGONAL THEOREM AND
RUSSELL S PARADOX 12 1.11 THE AXIOM OF CHOICE AND AXIOMATIC SET THEORY
13 1.12 ZORN S LEMMA 15 1.13 ORDINALS 18 2 TOPOLOGY 21 2.1 TOPOLOGICAL
SPACES 23 2.2 NEIGHBORHOODS AND CLOSURES 26 2.3 DENSE SUBSETS 28 2.4
NETS 29 2.5 FILTERS 32 2.6 NETS AND FILTERS 35 2.7 CONTINUOUS FUNCTIONS
36 2.8 COMPACTNESS 38 2.9 NETS VS. SEQUENCES 41 2.10 SEMICONTINUOUS
FUNCTIONS 43 2.11 SEPARATION PROPERTIES 44 2.12 COMPARING TOPOLOGIES 47
2.13 WEAK TOPOLOGIES 47 2.14 THE PRODUCT TOPOLOGY 50 2.15 POINTWISE AND
UNIFORM CONVERGENCE 53 XII CONTENTS 2.16 LOCALLY COMPACT SPACES 55 2.17
THE STONE-CECH COMPACTIFICATION 58 2.18 STONE-CECH COMPACTIFICATION OF A
DISCRETE SET 63 2.19 PARACOMPACT SPACES AND PARTITIONS OF UNITY 65 3
METRIZABLE SPACES 69 3.1 METRIC SPACES 70 3.2 COMPLETENESS 73 3.3
UNIFORMLY CONTINUOUS FUNCTIONS 76 3.4 SEMICONTINUOUS FUNCTIONS ON METRIC
SPACES 79 3.5 DISTANCE FUNCTIONS 80 3.6 EMBEDDINGS AND COMPLETIONS 84
3.7 COMPACTNESS AND COMPLETENESS 85 3.8 COUNTABLE PRODUCTS OF METRIC
SPACES 89 3.9 THE HILBERT CUBE AND METRIZATION 90 3.10 LOCALLY COMPACT
METRIZABLE SPACES 92 3.11 THE BAIRE CATEGORY THEOREM 93 3.12 CONTRACTION
MAPPINGS 95 3.13 THE CANTOR SET 98 3.14 THE BAIRE SPACE N N 101 3.15
UNIFORMITIES 108 3.16 THE HAUSDORF? DISTANCE 109 3.17 THE HAUSDORFF
METRIC TOPOLOGY 113 3.18 TOPOLOGIES FOR SPACES OF SUBSETS 119 3.19 THE
SPACE C(X, Y) 123 4 MEASURABILITY 127 4.1 ALGEBRAS OF SETS 129 4.2 RINGS
AND SEMIRINGS OF SETS 131 4.3 DYNKIN S LEMMA 135 4.4 THE BOREL
CR-ALGEBRA 137 4.5 MEASURABLE FUNCTIONS 139 4.6 THE SPACE OF MEASURABLE
FUNCTIONS 141 4.7 SIMPLE FUNCTIONS 144 4.8 THE CR-ALGEBRA INDUCED BY A
FUNCTION 147 4.9 PRODUCT STRUCTURES 148 4.10 CARATHEODORY FUNCTIONS 153
4.11 BOREL FUNCTIONS AND CONTINUITY 156 4.12 THE BAIRE CR-ALGEBRA 158 5
TOPOLOGICAL VECTOR SPACES 163 5.1 LINEAR TOPOLOGIES 166 5.2 ABSORBING
AND CIRCLED SETS 168 5.3 METRIZABLE TOPOLOGICAL VECTOR SPACES 172 5.4
THE OPEN MAPPING AND CLOSED GRAPH THEOREMS 175 5.5 FINITE DIMENSIONAL
TOPOLOGICAL VECTOR SPACES 177 CONTENTS XIII 5.6 CONVEX SETS 181 5.7
CONVEX AND CONCAVE FUNCTIONS 186 5.8 SUBLINEAR FUNCTIONS AND GAUGES 190
5.9 THE HAHN-BANACH EXTENSION THEOREM 195 5.10 SEPARATING HYPERPLANE
THEOREMS 197 5.11 SEPARATION BY CONTINUOUS FUNCTIONALS 201 5.12 LOCALLY
CONVEX SPACES AND SEMINORMS 204 5.13 SEPARATION IN LOCALLY CONVEX SPACES
207 5.14 DUAL PAIRS 211 5.15 TOPOLOGIES CONSISTENT WITH A GIVEN DUAL 213
5.16 POLARS 215 5.17 3-TOPOLOGIES 220 5.18 THE MACKEY TOPOLOGY 223 5.19
THE STRONG TOPOLOGY 223 6 NORMED SPACES 225 6.1 NORMED AND BANACH SPACES
227 6.2 LINEAR OPERATORS ON NORMED SPACES 229 6.3 THE NORM DUAL OF A
NORMED SPACE 230 6.4 THE UNIFORM BOUNDEDNESS PRINCIPLE 232 6.5 WEAK
TOPOLOGIES ON NORMED SPACES 235 6.6 METRIZABILITY OF WEAK TOPOLOGIES 237
6.7 CONTINUITY OF THE EVALUATION 241 6.8 ADJOINT OPERATORS 243 6.9
PROJECTIONS AND THE FIXED SPACE OF AN OPERATOR 244 6.10 HILBERT SPACES
246 7 CONVEXITY 251 7.1 EXTENDED-VALUED CONVEX FUNCTIONS 254 7.2 LOWER
SEMICONTINUOUS CONVEX FUNCTIONS 255 7.3 SUPPORT POINTS 258 7.4
SUBGRADIENTS 264 7.5 SUPPORTING HYPERPLANES AND CONES 268 7.6 CONVEX
FUNCTIONS ON FINITE DIMENSIONAL SPACES 271 7.7 SEPARATION AND SUPPORT IN
FINITE DIMENSIONAL SPACES 275 7.8 SUPPORTING CONVEX SUBSETS OF HILBERT
SPACES 280 7.9 THE BISHOP-PHELPS THEOREM 281 7.10 SUPPORT FUNCTIONALS
288 7.11 SUPPORT FUNCTIONALS AND THE HAUSDORFF METRIC 292 7.12 EXTREME
POINTS OF CONVEX SETS 294 7.13 QUASICONVEXITY 299 7.14 POLYTOPES AND
WEAK NEIGHBORHOODS 300 7.15 EXPOSED POINTS OF CONVEX SETS 305 XIV
CONTENTS 8 RIESZ SPACES 311 8.1 ORDERS, LATTICES, AND CONES 312 8.2
RIESZ SPACES 313 8.3 ORDER BOUNDED SETS 315 8.4 ORDER AND LATTICE
PROPERTIES 316 8.5 THE RIESZ DECOMPOSITION PROPERTY 319 8.6 DISJOINTNESS
320 8.7 RIESZ SUBSPACES AND IDEALS 321 8.8 ORDER CONVERGENCE AND ORDER
CONTINUITY 322 8.9 BANDS 324 8.10 POSITIVE FUNCTIONALS 325 8.11
EXTENDING POSITIVE FUNCTIONALS 330 8.12 POSITIVE OPERATORS 332 8.13
TOPOLOGICAL RIESZ SPACES 334 8.14 THE BAND GENERATED BY E 339 8.15
RIESZ PAIRS 340 8.16 SYMMETRIC RIESZ PAIRS 342 9 BANACH LATTICES 347 9.1
FRECHET AND BANACH LATTICES 348 9.2 THE STONE-WEIERSTRASS THEOREM 352
9.3 LATTICE HOMOMORPHISMS AND ISOMETRIES . 353 9.4 ORDER CONTINUOUS
NORMS 355 9.5 AM- AND AL-SPACES 357 9.6 THE INTERIOR OF THE POSITIVE
CONE 362 9.7 POSITIVE PROJECTIONS 364 9.8 THE CURIOUS AL-SPACE BV {) 365
10 CHARGES AND MEASURES 371 10.1 SET FUNCTIONS 374 10.2 LIMITS OF
SEQUENCES OF MEASURES 379 10.3 OUTER MEASURES AND MEASURABLE SETS 379
10.4 THE CARATHEODORY EXTENSION OF A MEASURE 381 10.5 MEASURE SPACES 387
10.6 LEBESGUE MEASURE 389 10.7 PRODUCT MEASURES 391 10.8 MEASURES ON R
392 10.9 ATOMS 395 10.10 THE AL-SPACE OF CHARGES 396 10.11 THE AL-SPACE
OF MEASURES 399 10.12 ABSOLUTE CONTINUITY 401 CONTENTS XV 11 INTEGRALS
403 11.1 THE INTEGRAL OF A STEP FUNCTION 404 11.2 FINITELY ADDITIVE
INTEGRATION OF BOUNDED FUNCTIONS 406 11.3 THE LEBESGUE INTEGRAL 408 11.4
CONTINUITY PROPERTIES OF THE LEBESGUE INTEGRAL 413 11.5 THE EXTENDED
LEBESGUE INTEGRAL 416 11.6 ITERATED INTEGRALS 418 11.7 THE RIEMANN
INTEGRAL 419 11.8 THE BOCHNER INTEGRAL 422 11.9 THE GELFAND INTEGRAL 428
11.10 THE DUNFORD AND PETTIS INTEGRALS 431 12 MEASURES AND TOPOLOGY 433
12.1 BOREL MEASURES AND REGULARITY 434 12.2 REGULAR BOREL MEASURES 438
12.3 THE SUPPORT OF A MEASURE 441 12.4 NONATOMIC BOREL MEASURES 443 12.5
ANALYTIC SETS 446 12.6 THE CHOQUET CAPACITY THEOREM 456 13 /^-SPACES 461
13.1 L^-NORMS 462 13.2 INEQUALITIES OF HOLDER AND MINKOWSKI 463 13.3
DENSE SUBSPACES OF L P -SPACES 466 13.4 SUBLATTICES OF L /; -SPACES 467
13.5 SEPARABLE L,-SPACES AND MEASURES 468 13.6 THE RADON-NIKODYM THEOREM
469 13.7 EQUIVALENT MEASURES 471 13.8 DUALS OF LP-SPACES 473 13.9
LYAPUNOV S CONVEXITY THEOREM 475 13.10 CONVERGENCE IN MEASURE 479 13.11
CONVERGENCE IN MEASURE IN L ; ,-SPACES 481 13.12 CHANGE OF VARIABLES 483
14 RIESZ REPRESENTATION THEOREMS 487 14.1 THE AM-SPACE B B (L) AND ITS
DUAL 488 14.2 THE DUAL OF C B (X) FOR NORMAL SPACES 491 14.3 THE DUAL OF
C C (X) FOR LOCALLY COMPACT SPACES 496 14.4 BAIRE VS. BOREL MEASURES 498
14.5 HOMOMORPHISMS BETWEEN C(X)-SPACES 500 XVI CONTENTS 15 PROBABILITY
MEASURES 505 15.1 THE WEAK* TOPOLOGY ON 0 (X) 506 15.2 EMBEDDING X IN
0 (X) 512 15.3 PROPERTIES OF 0 (X) 513 15.4 THE MANY FACES OF ? (X)
517 15.5 COMPACTNESS IN ? (X) 518 15.6 THE KOLMOGOROV EXTENSION THEOREM
519 16 SPACES OF SEQUENCES 525 16.1 THE BASIC SEQUENCE SPACES 526 16.2
THE SEQUENCE SPACES R N AND 527 16.3 THE SEQUENCE SPACE C 0 529 16.4 THE
SEQUENCE SPACE C 531 16.5 THE /^-SPACES 533 16.6 AND THE SYMMETRIC
RIESZ PAIR (IFOO,^|) 537 16.7 THE SEQUENCE SPACE C 538 16.8 MORE ON * *
= BA(N) 543 16.9 EMBEDDING SEQUENCE SPACES 546 16.10 BANACH-MAZUR LIMITS
AND INVARIANT MEASURES 550 16.11 SEQUENCES OF VECTOR SPACES 552 17
CORRESPONDENCES 555 17.1 BASIC DEFINITIONS 556 17.2 CONTINUITY OF
CORRESPONDENCES 558 17.3 HEMICONTINUITY AND NETS 563 17.4 OPERATIONS ON
CORRESPONDENCES 566 17.5 THE MAXIMUM THEOREM 569 17.6 VECTOR-VALUED
CORRESPONDENCES 571 17.7 DEMICONTINUOUS CORRESPONDENCES 574 17.8
KNASTER-KURATOWSKI-MAZURKIEWICZ MAPPINGS 577 17.9 FIXED POINT THEOREMS
581 17.10 CONTRACTION CORRESPONDENCES 585 17.11 CONTINUOUS SELECTORS 587
18 MEASURABLE CORRESPONDENCES 591 18.1 MEASURABILITY NOTIONS 592 18.2
COMPACT-VALUED CORRESPONDENCES AS FUNCTIONS 597 18.3 MEASURABLE
SELECTORS 600 18.4 CORRESPONDENCES WITH MEASURABLE GRAPH 606 18.5
CORRESPONDENCES WITH COMPACT CONVEX VALUES 609 18.6 INTEGRATION OF
CORRESPONDENCES 614 CONTENTS XVII 19 MARKOV TRANSITIONS 621 19.1 MARKOV
AND STOCHASTIC OPERATORS 623 19.2 MARKOV TRANSITIONS AND KERNELS 625
19.3 CONTINUOUS MARKOV TRANSITIONS 631 19.4 INVARIANT MEASURES 631 19.5
ERGODIC MEASURES 636 19.6 MARKOV TRANSITION CORRESPONDENCES 638 19.7
RANDOM FUNCTIONS 641 19.8 DILATIONS 645 19.9 MORE ON MARKOV OPERATORS
650 19.10 A NOTE ON DYNAMICAL SYSTEMS 652 20 ERGODICITY 655 20.1
MEASURE-PRESERVING TRANSFORMATIONS AND ERGODICITY 656 20.2 BIRKHOFF S
ERGODIC THEOREM 659 20.3 ERGODIC OPERATORS 661 REFERENCES 667 INDEX 681
|
| adam_txt |
CHARALAMBOS D. ALIPRANTIS KIM C. BORDER INFINITE DIMENSIONAL ANALYSIS A
HITCHHIKER'S GUIDE THIRD EDITION WITH 38 FIGURES AND 1 TABLE _J
SPRINGER CONTENTS PREFACE TO THE THIRD EDITION VII A FOREWORD TO THE
PRACTICAL XIX 1 ODDS AND ENDS 1 1.1 NUMBERS 1 1.2 SETS 2 1.3 RELATIONS,
CORRESPONDENCES, AND FUNCTIONS 4 1.4 A BESTIARY OF RELATIONS 5 1.5
EQUIVALENCE RELATIONS 7 1.6 ORDERS AND SUCH 7 1.7 REAL FUNCTIONS 8 1.8
DUALITY OF EVALUATION 9 1.9 INFINITIES 10 1.10 THE DIAGONAL THEOREM AND
RUSSELL'S PARADOX 12 1.11 THE AXIOM OF CHOICE AND AXIOMATIC SET THEORY
13 1.12 ZORN'S LEMMA 15 1.13 ORDINALS 18 2 TOPOLOGY 21 2.1 TOPOLOGICAL
SPACES 23 2.2 NEIGHBORHOODS AND CLOSURES 26 2.3 DENSE SUBSETS 28 2.4
NETS 29 2.5 FILTERS 32 2.6 NETS AND FILTERS 35 2.7 CONTINUOUS FUNCTIONS
36 2.8 COMPACTNESS 38 2.9 NETS VS. SEQUENCES 41 2.10 SEMICONTINUOUS
FUNCTIONS 43 2.11 SEPARATION PROPERTIES 44 2.12 COMPARING TOPOLOGIES 47
2.13 WEAK TOPOLOGIES 47 2.14 THE PRODUCT TOPOLOGY 50 2.15 POINTWISE AND
UNIFORM CONVERGENCE 53 XII CONTENTS 2.16 LOCALLY COMPACT SPACES 55 2.17
THE STONE-CECH COMPACTIFICATION 58 2.18 STONE-CECH COMPACTIFICATION OF A
DISCRETE SET 63 2.19 PARACOMPACT SPACES AND PARTITIONS OF UNITY 65 3
METRIZABLE SPACES 69 3.1 METRIC SPACES 70 3.2 COMPLETENESS 73 3.3
UNIFORMLY CONTINUOUS FUNCTIONS 76 3.4 SEMICONTINUOUS FUNCTIONS ON METRIC
SPACES 79 3.5 DISTANCE FUNCTIONS 80 3.6 EMBEDDINGS AND COMPLETIONS 84
3.7 COMPACTNESS AND COMPLETENESS 85 3.8 COUNTABLE PRODUCTS OF METRIC
SPACES 89 3.9 THE HILBERT CUBE AND METRIZATION 90 3.10 LOCALLY COMPACT
METRIZABLE SPACES 92 3.11 THE BAIRE CATEGORY THEOREM 93 3.12 CONTRACTION
MAPPINGS 95 3.13 THE CANTOR SET 98 3.14 THE BAIRE SPACE N N 101 3.15
UNIFORMITIES 108 3.16 THE HAUSDORF? DISTANCE 109 3.17 THE HAUSDORFF
METRIC TOPOLOGY 113 3.18 TOPOLOGIES FOR SPACES OF SUBSETS 119 3.19 THE
SPACE C(X, Y) 123 4 MEASURABILITY 127 4.1 ALGEBRAS OF SETS 129 4.2 RINGS
AND SEMIRINGS OF SETS 131 4.3 DYNKIN'S LEMMA 135 4.4 THE BOREL
CR-ALGEBRA 137 4.5 MEASURABLE FUNCTIONS 139 4.6 THE SPACE OF MEASURABLE
FUNCTIONS 141 4.7 SIMPLE FUNCTIONS 144 4.8 THE CR-ALGEBRA INDUCED BY A
FUNCTION 147 4.9 PRODUCT STRUCTURES 148 4.10 CARATHEODORY FUNCTIONS 153
4.11 BOREL FUNCTIONS AND CONTINUITY 156 4.12 THE BAIRE CR-ALGEBRA 158 5
TOPOLOGICAL VECTOR SPACES 163 5.1 LINEAR TOPOLOGIES 166 5.2 ABSORBING
AND CIRCLED SETS 168 5.3 METRIZABLE TOPOLOGICAL VECTOR SPACES 172 5.4
THE OPEN MAPPING AND CLOSED GRAPH THEOREMS 175 5.5 FINITE DIMENSIONAL
TOPOLOGICAL VECTOR SPACES 177 CONTENTS XIII 5.6 CONVEX SETS 181 5.7
CONVEX AND CONCAVE FUNCTIONS 186 5.8 SUBLINEAR FUNCTIONS AND GAUGES 190
5.9 THE HAHN-BANACH EXTENSION THEOREM 195 5.10 SEPARATING HYPERPLANE
THEOREMS 197 5.11 SEPARATION BY CONTINUOUS FUNCTIONALS 201 5.12 LOCALLY
CONVEX SPACES AND SEMINORMS 204 5.13 SEPARATION IN LOCALLY CONVEX SPACES
207 5.14 DUAL PAIRS 211 5.15 TOPOLOGIES CONSISTENT WITH A GIVEN DUAL 213
5.16 POLARS 215 5.17 3-TOPOLOGIES 220 5.18 THE MACKEY TOPOLOGY 223 5.19
THE STRONG TOPOLOGY 223 6 NORMED SPACES 225 6.1 NORMED AND BANACH SPACES
227 6.2 LINEAR OPERATORS ON NORMED SPACES 229 6.3 THE NORM DUAL OF A
NORMED SPACE 230 6.4 THE UNIFORM BOUNDEDNESS PRINCIPLE 232 6.5 WEAK
TOPOLOGIES ON NORMED SPACES 235 6.6 METRIZABILITY OF WEAK TOPOLOGIES 237
6.7 CONTINUITY OF THE EVALUATION 241 6.8 ADJOINT OPERATORS 243 6.9
PROJECTIONS AND THE FIXED SPACE OF AN OPERATOR 244 6.10 HILBERT SPACES
246 7 CONVEXITY 251 7.1 EXTENDED-VALUED CONVEX FUNCTIONS 254 7.2 LOWER
SEMICONTINUOUS CONVEX FUNCTIONS 255 7.3 SUPPORT POINTS 258 7.4
SUBGRADIENTS 264 7.5 SUPPORTING HYPERPLANES AND CONES 268 7.6 CONVEX
FUNCTIONS ON FINITE DIMENSIONAL SPACES 271 7.7 SEPARATION AND SUPPORT IN
FINITE DIMENSIONAL SPACES 275 7.8 SUPPORTING CONVEX SUBSETS OF HILBERT
SPACES 280 7.9 THE BISHOP-PHELPS THEOREM 281 7.10 SUPPORT FUNCTIONALS
288 7.11 SUPPORT FUNCTIONALS AND THE HAUSDORFF METRIC 292 7.12 EXTREME
POINTS OF CONVEX SETS 294 7.13 QUASICONVEXITY 299 7.14 POLYTOPES AND
WEAK NEIGHBORHOODS 300 7.15 EXPOSED POINTS OF CONVEX SETS 305 XIV
CONTENTS 8 RIESZ SPACES 311 8.1 ORDERS, LATTICES, AND CONES 312 8.2
RIESZ SPACES 313 8.3 ORDER BOUNDED SETS 315 8.4 ORDER AND LATTICE
PROPERTIES 316 8.5 THE RIESZ DECOMPOSITION PROPERTY 319 8.6 DISJOINTNESS
320 8.7 RIESZ SUBSPACES AND IDEALS 321 8.8 ORDER CONVERGENCE AND ORDER
CONTINUITY 322 8.9 BANDS 324 8.10 POSITIVE FUNCTIONALS 325 8.11
EXTENDING POSITIVE FUNCTIONALS 330 8.12 POSITIVE OPERATORS 332 8.13
TOPOLOGICAL RIESZ SPACES 334 8.14 THE BAND GENERATED BY E' 339 8.15
RIESZ PAIRS 340 8.16 SYMMETRIC RIESZ PAIRS 342 9 BANACH LATTICES 347 9.1
FRECHET AND BANACH LATTICES 348 9.2 THE STONE-WEIERSTRASS THEOREM 352
9.3 LATTICE HOMOMORPHISMS AND ISOMETRIES . 353 9.4 ORDER CONTINUOUS
NORMS 355 9.5 AM- AND AL-SPACES 357 9.6 THE INTERIOR OF THE POSITIVE
CONE 362 9.7 POSITIVE PROJECTIONS 364 9.8 THE CURIOUS AL-SPACE BV {) 365
10 CHARGES AND MEASURES 371 10.1 SET FUNCTIONS 374 10.2 LIMITS OF
SEQUENCES OF MEASURES 379 10.3 OUTER MEASURES AND MEASURABLE SETS 379
10.4 THE CARATHEODORY EXTENSION OF A MEASURE 381 10.5 MEASURE SPACES 387
10.6 LEBESGUE MEASURE 389 10.7 PRODUCT MEASURES 391 10.8 MEASURES ON R"
392 10.9 ATOMS 395 10.10 THE AL-SPACE OF CHARGES 396 10.11 THE AL-SPACE
OF MEASURES 399 10.12 ABSOLUTE CONTINUITY 401 CONTENTS XV 11 INTEGRALS
403 11.1 THE INTEGRAL OF A STEP FUNCTION 404 11.2 FINITELY ADDITIVE
INTEGRATION OF BOUNDED FUNCTIONS 406 11.3 THE LEBESGUE INTEGRAL 408 11.4
CONTINUITY PROPERTIES OF THE LEBESGUE INTEGRAL 413 11.5 THE EXTENDED
LEBESGUE INTEGRAL 416 11.6 ITERATED INTEGRALS 418 11.7 THE RIEMANN
INTEGRAL 419 11.8 THE BOCHNER INTEGRAL 422 11.9 THE GELFAND INTEGRAL 428
11.10 THE DUNFORD AND PETTIS INTEGRALS 431 12 MEASURES AND TOPOLOGY 433
12.1 BOREL MEASURES AND REGULARITY 434 12.2 REGULAR BOREL MEASURES 438
12.3 THE SUPPORT OF A MEASURE 441 12.4 NONATOMIC BOREL MEASURES 443 12.5
ANALYTIC SETS 446 12.6 THE CHOQUET CAPACITY THEOREM 456 13 /^-SPACES 461
13.1 L^-NORMS 462 13.2 INEQUALITIES OF HOLDER AND MINKOWSKI 463 13.3
DENSE SUBSPACES OF L P -SPACES 466 13.4 SUBLATTICES OF L /; -SPACES 467
13.5 SEPARABLE L,-SPACES AND MEASURES 468 13.6 THE RADON-NIKODYM THEOREM
469 13.7 EQUIVALENT MEASURES 471 13.8 DUALS OF LP-SPACES 473 13.9
LYAPUNOV'S CONVEXITY THEOREM 475 13.10 CONVERGENCE IN MEASURE 479 13.11
CONVERGENCE IN MEASURE IN L ; ,-SPACES 481 13.12 CHANGE OF VARIABLES 483
14 RIESZ REPRESENTATION THEOREMS 487 14.1 THE AM-SPACE B B (L) AND ITS
DUAL 488 14.2 THE DUAL OF C B (X) FOR NORMAL SPACES 491 14.3 THE DUAL OF
C C (X) FOR LOCALLY COMPACT SPACES 496 14.4 BAIRE VS. BOREL MEASURES 498
14.5 HOMOMORPHISMS BETWEEN C(X)-SPACES 500 XVI CONTENTS 15 PROBABILITY
MEASURES 505 15.1 THE WEAK* TOPOLOGY ON 0 (X) 506 15.2 EMBEDDING X IN
0 (X) 512 15.3 PROPERTIES OF 0 (X) 513 15.4 THE MANY FACES OF ? (X)
517 15.5 COMPACTNESS IN ? (X) 518 15.6 THE KOLMOGOROV EXTENSION THEOREM
519 16 SPACES OF SEQUENCES 525 16.1 THE BASIC SEQUENCE SPACES 526 16.2
THE SEQUENCE SPACES R N AND 527 16.3 THE SEQUENCE SPACE C 0 529 16.4 THE
SEQUENCE SPACE C 531 16.5 THE /^-SPACES 533 16.6 \ AND THE SYMMETRIC
RIESZ PAIR (IFOO,^|) 537 16.7 THE SEQUENCE SPACE C 538 16.8 MORE ON *'*
= BA(N) 543 16.9 EMBEDDING SEQUENCE SPACES 546 16.10 BANACH-MAZUR LIMITS
AND INVARIANT MEASURES 550 16.11 SEQUENCES OF VECTOR SPACES 552 17
CORRESPONDENCES 555 17.1 BASIC DEFINITIONS 556 17.2 CONTINUITY OF
CORRESPONDENCES 558 17.3 HEMICONTINUITY AND NETS 563 17.4 OPERATIONS ON
CORRESPONDENCES 566 17.5 THE MAXIMUM THEOREM 569 17.6 VECTOR-VALUED
CORRESPONDENCES 571 17.7 DEMICONTINUOUS CORRESPONDENCES 574 17.8
KNASTER-KURATOWSKI-MAZURKIEWICZ MAPPINGS 577 17.9 FIXED POINT THEOREMS
581 17.10 CONTRACTION CORRESPONDENCES 585 17.11 CONTINUOUS SELECTORS 587
18 MEASURABLE CORRESPONDENCES 591 18.1 MEASURABILITY NOTIONS 592 18.2
COMPACT-VALUED CORRESPONDENCES AS FUNCTIONS 597 18.3 MEASURABLE
SELECTORS 600 18.4 CORRESPONDENCES WITH MEASURABLE GRAPH 606 18.5
CORRESPONDENCES WITH COMPACT CONVEX VALUES 609 18.6 INTEGRATION OF
CORRESPONDENCES 614 CONTENTS XVII 19 MARKOV TRANSITIONS 621 19.1 MARKOV
AND STOCHASTIC OPERATORS 623 19.2 MARKOV TRANSITIONS AND KERNELS 625
19.3 CONTINUOUS MARKOV TRANSITIONS 631 19.4 INVARIANT MEASURES 631 19.5
ERGODIC MEASURES 636 19.6 MARKOV TRANSITION CORRESPONDENCES 638 19.7
RANDOM FUNCTIONS 641 19.8 DILATIONS 645 19.9 MORE ON MARKOV OPERATORS
650 19.10 A NOTE ON DYNAMICAL SYSTEMS 652 20 ERGODICITY 655 20.1
MEASURE-PRESERVING TRANSFORMATIONS AND ERGODICITY 656 20.2 BIRKHOFF'S
ERGODIC THEOREM 659 20.3 ERGODIC OPERATORS 661 REFERENCES 667 INDEX 681 |
| any_adam_object | 1 |
| any_adam_object_boolean | 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 | BV021758050 |
| classification_rvk | QH 150 SK 130 SK 280 SK 600 |
| ctrlnum | (OCoLC)470958494 (DE-599)BVBBV021758050 |
| 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 | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | third edition |
| format | Book |
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| id | DE-604.BV021758050 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:34:12Z |
| indexdate | 2024-07-09T20:43:23Z |
| institution | BVB |
| isbn | 3540295860 9783540295860 9783540326960 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014971184 |
| oclc_num | 470958494 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-29T DE-19 DE-BY-UBM DE-11 DE-83 DE-739 |
| owner_facet | DE-824 DE-703 DE-29T DE-19 DE-BY-UBM DE-11 DE-83 DE-739 |
| physical | xxii, 703 Seiten |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| spelling | Aliprantis, Charalambos D. 1946-2009 (DE-588)121199010 aut Infinite dimensional analysis a hitchhiker's guide Charalambos D. Aliprantis ; Kim C. Border third edition Berlin ; Heidelberg ; New York Springer [2006] © 2006 xxii, 703 Seiten txt rdacontent n rdamedia nc rdacarrier Analyse fonctionnelle ram Funktionalanalysis swd Mathématiques économiques ram Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 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 b DE-604 Border, Kim C. 1952- (DE-588)121199037 aut Erscheint auch als Online-Ausgabe 978-3-540-29587-7 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aliprantis, Charalambos D. 1946-2009 Border, Kim C. 1952- Infinite dimensional analysis a hitchhiker's guide Analyse fonctionnelle ram Funktionalanalysis swd Mathématiques économiques ram Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Analysis (DE-588)4001865-9 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4207852-0 (DE-588)4001865-9 (DE-588)4066472-7 (DE-588)4018916-8 |
| 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_exact_search_txtP | 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 | Analyse fonctionnelle ram Funktionalanalysis swd Mathématiques économiques ram Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Analysis (DE-588)4001865-9 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Funktionalanalysis Mathématiques économiques Unendlichdimensionaler Raum Analysis Wirtschaftsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971184&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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