Foundations of abstract analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2013
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 748 S. graph. Darst. |
| ISBN: | 9781461459613 |
Internformat
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| 245 | 1 | 0 | |a Foundations of abstract analysis |c Jewgeni H. Dshalalow |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Foundations of abstract analysis
Autor: Dshalalow, Jewgeni H
Jahr: 2013
Contents
Preface vii
PARTI
Principles of Set Theory and
Point-Set Topology 1
Chapter 1 Set-Theoretic and Algebraic Preliminaries 3
1. Sets and Basic Notation 3
2. Functions 14
3. Set Operations under Maps 23
4. Relations and Well-Ordering Principle 29
5. Cartesian Product 42
6. Cardinality 58
7. Basic Algebraic Structures 66
8. More about Vector Spaces 85
Chapter 2 Analysis of Metric Spaces 93
1. Definitions and Notations 94
2. The Structure of Metric Spaces 101
3. Convergence in Metric Spaces 112
4. Continuous Mappings in Metric Spaces 117
5. Complete Metric Spaces 132
6. Compactness 138
7. Normed Vector Spaces 149
8. Finite-Dimensional Normed Vector Spaces 160
Chapter 3 Elements of Point-Set Topology 171
1. Topological Spaces 171
2. Bases and Subbases for Topological Spaces 188
3. Hausdorff Topological Spaces 197
4. Continuity in Topological Spaces 203
5. Product Topology 213
6. Notes on Subspaces and Compactness 226
PART II
Measure Theory and Abstract Integration 237
Chapter 4 Measurable Spaces and Measurable Functions 239
1. Systems of Sets 240
2. System s Generators 247
3. Measurable Functions 255
Chapter 5 Measures 261
1. Set Functions 263
2. Extension of Set Functions to a Measure 283
3. Lebesgue and Lebesgue-Stieltjes Measures 313
4. Image Measures 336
5. Extended Real-Valued Measurable Functions 343
6. Simple Functions 354
Chapter 6 Integration in Abstract Spaces 361
1. Integration on C_1(^, E) 362
2. Main Convergence Theorems 382
3. Lebesgue and Riemann Integrals on R 399
4. Integration with Respect to Image Measures 416
5. Positive Measures Generated by Integrals. Absolute
Continuity 422
6. Signed Measures 434
7. Complex Measures and Integration 458
8. Radon-Nikodym Theorem for Signed and Complex
Measures and its Applications 471
9. Measures and Integration on Finite Product Spaces 498
PART III
Supplementary Materials 533
Chapter 7 Solutions to Selected Problems 535
Bibliography 715
List of Symbols 721
Index of Names and Terms 731
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| discipline | Mathematik |
| edition | 2. ed. |
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| indexdate | 2024-07-10T00:32:04Z |
| institution | BVB |
| isbn | 9781461459613 |
| language | English |
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| physical | XIII, 748 S. graph. Darst. |
| publishDate | 2013 |
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| spelling | Dshalalow, Jewgeni H. Verfasser (DE-588)133145379 aut Foundations of abstract analysis Jewgeni H. Dshalalow 2. ed. New York, NY [u.a.] Springer 2013 XIII, 748 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mengenlehre (DE-588)4074715-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Analysis (DE-588)4001865-9 s Maßtheorie (DE-588)4074626-4 s Mengenlehre (DE-588)4074715-3 s Integrationstheorie (DE-588)4138369-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025683431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dshalalow, Jewgeni H. Foundations of abstract analysis Mengenlehre (DE-588)4074715-3 gnd Analysis (DE-588)4001865-9 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074715-3 (DE-588)4001865-9 (DE-588)4138369-2 (DE-588)4074626-4 |
| title | Foundations of abstract analysis |
| title_auth | Foundations of abstract analysis |
| title_exact_search | Foundations of abstract analysis |
| title_full | Foundations of abstract analysis Jewgeni H. Dshalalow |
| title_fullStr | Foundations of abstract analysis Jewgeni H. Dshalalow |
| title_full_unstemmed | Foundations of abstract analysis Jewgeni H. Dshalalow |
| title_short | Foundations of abstract analysis |
| title_sort | foundations of abstract analysis |
| topic | Mengenlehre (DE-588)4074715-3 gnd Analysis (DE-588)4001865-9 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Mengenlehre Analysis Integrationstheorie Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025683431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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