Modern analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
1998
|
| Series: | Studies in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis http://www.zentralblatt-math.org/zmath/en/search/?an=0893.46001 Inhaltsverzeichnis |
| Physical Description: | 572 S. graph. Darst. |
| ISBN: | 084937166X |
Staff View
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Record in the Search Index
| _version_ | 1804126681596690432 |
|---|---|
| adam_text | IMAGE 1
KENNETH KUTTLER
MICHIGAN TECHNOLOGICAL UNIVERSITY
MODERN ANALYSIS
CRC PRESS * BOCA RATON BOSTON NEW YORK WASHINGTON LONDON
M2DERSACHS? STAATS.U.UNIV.- BIBLIOTHEK GOTTIJNGEN
IMAGE 2
CONTENTS
1 SET-THEORY AND GENERAL TOPOLOGY 1
1 SET THEORY 1
2 GENERAL TOPOLOGY 4
3 URYSOHN S LEMMA 9
4 EXERCISES 12
2 COMPACTNESS AND CONTINUOUS FUNCTIONS 17
1 COMPACTNESS IN METRIC SPACE 17
2 COMPACTNESS IN SPACES OF CONTINUOUS FUNCTIONS 21
3 STONE WEIERSTRASS THEOREM 24
4 EXERCISES 29
3 BANACH SPACES 33
1 BAIRE CATEGORY THEOREM 33
2 UNIFORM BOUNDEDNESS CLOSED GRAPH AND OPEN MAPPING THEOREMS 36
3 HAHN BANACH THEOREM 40
4 EXERCISES 45
4 HILBERT SPACES 49
1 FINITE DIMENSIONAL NORMED LINEAR SPACE 53
2 UNIFORMLY CONVEX BANACH SPACES 55
3 EXERCISES 60
5 CALCULUS IN BANACH SPACE 63
1 THE DERIVATIVE 63
2 FINITE DIMENSIONS 65
3 HIGHER ORDER DERIVATIVES 68
4 INVERSE FUNCTION THEOREM 70
5 ORDINARY DIFFERENTIAL EQUATIONS 78
6 EXERCISES 80
6 LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES 87
1 SEPARATION THEOREMS 91
2 THE WEAK AND WEAK* TOPOLOGIES 97
3 THE TYCHONOFF FIXED POINT THEOREM 105
4 SET-VALUED MAPS 110
5 FINITE DIMENSIONAL SPACES 115
6 EXERCISES. . . 119
7 MEASURES AND MEASURABLE FUNCTIONS 123
1 R ALGEBRAS 123
2 MONOTONE CLASSES AND ALGEBRAS 123
IMAGE 3
2 MONOTONE CLASSES AND ALGEBRAS 123
3 EXERCISES 132
8 THE ABSTRACT LEBESGUE INTEGRAL 135
1 THE SPACE L 1 139
2 DOUBLE SUMS OF NONNEGATIVE TERMS 144
3 EXERCISES 145
9 THE CONSTRUCTION OF MEASURES 149
1 OUTER MEASURES 149
2 REGULAR MEASURES 154
3 LEBESGUE MEASURE ON M 1 168
4 EXERCISES 168
10 LEBESGUE MEASURE 171
1 LEBESGUE MEASURE 171
2 ITERATED INTEGRALS 175
3 CHANGE OF VARIABLES 177
4 POLAR COORDINATES 183
1 5 EXERCISES 186
11 PRODUCT MEASURE 189
1 COMPLETION OF PRODUCT MEASURE 195
2 EXERCISES 199
12 THE U SPACES 203
1 BASIC INEQUALITIES AND PROPERTIES 203
2 DENSITY OF SIMPLE FUNCTIONS 207
3 CONTINUITY OF TRANSLATION 209
4 SEPARABILITY 210
5 MOLLIFIERS AND DENSITY OF SMOOTH FUNCTIONS 211
6 EXERCISES 213
13 REPRESENTATION THEOREMS 219
1 RADON NIKODYM THEOREM 219
2 VECTOR MEASURES 221
3 REPRESENTATION THEOREMS FOR THE DUAL SPACE OF 1/ THE A FINITE CASE :
226
4 RIESZ REPRESENTATION THEOREM FOR NON A FINITE MEASURE SPACES 232
5 THE DUAL SPACE OF C (X) 237
6 EXERCISES. . .^. 241
14 FUNDAMENTAL THEOREM OF CALCULUS 245
1 THE VITALI COVERING THEOREM 245
IMAGE 4
2 DIFFERENTIATION WITH RESPECT TO LEBESGUE MEASURE 247
3 THE CHANGE OF VARIABLES THEOREM FOR MULTIPLE INTEGRALS . . .. 251 4
EXERCISES 259
15 GENERAL RADON MEASURES 263
1 BESICOVITCH COVERING THEOREM 263
2 DIFFERENTIATION WITH RESPECT TO RADON MEASURES 268
3 SLICING MEASURES 271
4 YOUNG MEASURES 277
5 EXERCISES 281
16 FOURIER TRANSFORMS 283
1 THE SCHWARTZ CLASS 283
2 FOURIER TRANSFORMS OF FUNCTIONS IN I? (M N ) 288
3 TEMPERED DISTRIBUTIONS 293
4 EXERCISES 299
17 PROBABILITY 303
1 RANDOM VECTORS 303
2 CONDITIONAL PROBABILITY AND INDEPENDENCE 308
3 CONDITIONAL EXPECTATION 316
4 CONDITIONAL EXPECTATION GIVEN A CR ALGEBRA 320
5 STRONG LAW OF LARGE NUMBERS 330
6 THE NORMAL DISTRIBUTION 335
7 THE CENTRAL LIMIT THEOREM 338
8 THE CONTINUITY THEOREM 342
9 EXERCISES 348
18 WEAK DERIVATIVES 355
1 TEST FUNCTIONS AND WEAK DERIVATIVES 355
2 WEAK DERIVATIVES IN L V LOC 359
3 MORREY S INEQUALITY 361
4 RADEMACHER S THEOREM 363
5 EXERCISES 366
19 HAUSDORFF MEASURES 371
1 STEINER SYMMETRIZATION 373
2 THE ISODIAMETRIC INEQUALITY 375
3 HAUSDORFF MEASURES 377
4 PROPERTIES OF HAUSDORFF MEASURE 378
20 THE AREA FORMULA ^ 387
1 LIPSCHITZ MAPPINGS 387
2 THE AREA FORMULA FOR ONE TO ONE LIPSCHITZ MAPPINGS 395
3 MAPPINGS THAT ARE NOT ONE TO ONE 398
IMAGE 5
4 SURFACE MEASURE 402
5 THE DIVERGENCE THEOREM 405
6 EXERCISES 412
21 THE COAREA FORMULA 419
1 A DETERMINANT IDENTITY 420
2 THE COAREA FORMULA 421
3 CHANGE OF VARIABLES 432
4 EXERCISES 433
22 FOURIER ANALYSIS IN E 435
1 THE MARCINKIEWICZ INTERPOLATION THEOREM 435
2 THE CALDERON ZYGMUND DECOMPOSITION 438
3 MIHLIN S THEOREM 440
4 SINGULAR INTEGRALS 453
5 THE HELMHOLTZ DECOMPOSITION OF VECTOR FIELDS 462
6 EXERCISES 469
23 INTEGRATION FOR VECTOR VALUED FUNCTIONS 475
1 STRONG AND WEAK MEASURABILITY 475
2 THE BOCHNER INTEGRAL 481
3 MEASURABLE REPRESENTATIVES 488
4 VECTOR MEASURES 490
5 THE RIESZ REPRESENTATION THEOREM 494
6 EXERCISES 499
24 CONVEX FUNCTIONS 503
1 CONTINUITY PROPERTIES OF CONVEX FUNCTIONS 503
2 SEPARATION PROPERTIES 506
3 CONJUGATE FUNCTIONS 509
4 SUBGRADIENTS 511
5 HILBERT SPACE 519
6 EXERCISES 524
APPENDIX 1: THE HAUSDORFF MAXIMAL THEOREM 529 1 EXERCISES 532
APPENDIX 2: STONE S THEOREM AND PARTITIONS OF UNITY 535
1 GENERAL PARTITIONS OF UNITY 540
2 A GENERAL METRIZATION THEOREM 541
APPENDIX 3: TAYLOR SERIES AND ANALYTIC FUNCTIONS 545 1 TAYLOR S FORMULA
545
2 ANALYTIC FUNCTIONS 546
IMAGE 6
3 ORDINARY DIFFERENTIAL EQUATIONS 552
APPENDIX 4: THE BROUWER FIXED POINT THEOREM 557
REFERENCES 561
INDEX 569
|
| any_adam_object | 1 |
| author | Kuttler, Kenneth |
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| dewey-full | 51521 515 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515 21 515 |
| dewey-search | 515 21 515 |
| dewey-sort | 3515 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:21:19Z |
| institution | BVB |
| isbn | 084937166X |
| language | English |
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| physical | 572 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | CRC Press |
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| series2 | Studies in advanced mathematics |
| spelling | Kuttler, Kenneth Verfasser aut Modern analysis Kenneth Kuttler Boca Raton [u.a.] CRC Press 1998 572 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 http://www.gbv.de/dms/goettingen/233496009.pdf Inhaltsverzeichnis DE-601 http://www.zentralblatt-math.org/zmath/en/search/?an=0893.46001 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008178315&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuttler, Kenneth Modern analysis Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Modern analysis |
| title_auth | Modern analysis |
| title_exact_search | Modern analysis |
| title_full | Modern analysis Kenneth Kuttler |
| title_fullStr | Modern analysis Kenneth Kuttler |
| title_full_unstemmed | Modern analysis Kenneth Kuttler |
| title_short | Modern analysis |
| title_sort | modern analysis |
| topic | Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Analysis |
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