Real analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Carbondale u.a.
Southern Ill. Univ. Pr.
1976
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 581 S. |
| ISBN: | 0809307278 |
Internformat
MARC
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| 245 | 1 | 0 | |a Real analysis |
| 264 | 1 | |a Carbondale u.a. |b Southern Ill. Univ. Pr. |c 1976 | |
| 300 | |a XII, 581 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 7 | |a Fonctions d'une variable réelle |2 ram | |
| 650 | 4 | |a Fonctions de variables réelles | |
| 650 | 4 | |a Functions of real variables | |
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Datensatz im Suchindex
| _version_ | 1804120761500172288 |
|---|---|
| adam_text | Contents
Preface xi
CHAPTER 1: SET THEORY
1.1 Introduction 1
1.2 Operations on Sets 5
1.3 Functions 7
1.4 Relations 13
1.5 Partial Ordering 17
1.6 Countable Sets 18
1.7 Cardinal Numbers 22
1.8 Operations on Cardinal Numbers 26
1.9 Algebra of Sets 30
1.10 The Axiom of Choice and Some of Its
Equivalent Formulations 33
1.11 Ordinal Numbers 36
Problems 45
CHAPTER 2: THE REAL NUMBERS
2.1 Fundamental Structures in Mathematics 53
2.2 Groups—Rings—Fields 54
2.3 Isomorphism of Mathematical Systems 57
2.4 The Extended Real Number System 63
CONTENTS viii
2.5 Topology of the Real Line 65
2.6 Continuous Functions 80
2.7 Semicontinuous Functions 87
2.8 The Cantor Ternary Set 89
2.9 Borel Sets 91
Problems 93
CHAPTER 3: LEBESGUE INTEGRAL
3.1 Introduction 104
3.2 Lebesgue Measure 107
3.3 Existence of a Nonmeasurable Set 119
3.4 Measurable Functions 121
3.5 Approximation Theorems 127
3.6 The Lebesgue Integral of a Bounded
Function Over a Set of Finite Measure 139
3.7 The Lebesgue Integral of a Nonnegative
Function 148
3.8 The General Lebesgue Integral 158
3.9 Further Comparison Between Riemann
and Lebesgue Integrals 167
Problems 169
CHAPTER 4: RELATION BETWEEN DIFFERENTIATION
AND INTEGRATION
4.1 Introduction 181
4.2 Functions of Bounded Variation 182
4.3 Differentiation of Monotone Functions 187
4.4 The Derivative of an Indefinite Integral 198
4.5 Absolutely Continuous Functions 205
Problems 211
CHAPTER 5: METRIC SPACES
5.1 Introduction 217
CONTENTS ix
5.2 Isometries 220
5.3 Open and Closed Sets 222
5.4 Continuous Mappings—Homeomorphisms 229
5.5 Equivalent Metrics 233
5.6 Limits—Convergence—Completeness 233
5.7 Uniformly Continuous Mappings 247
5.8 Extension of Mappings 250
5.9 The Method of Successive Approximations 252
5.10 Compact Metric Spaces and the Bolzano
Weierstrass Theorem 257
5.11 Equicontinuous Spaces of Functions 264
5.12 Category 271
Problems 276
CHAPTER 6: LP SPACES
6.1 Introduction 293
6.2 The Holder and Minkowski Inequalities 294
6.3 Convergence in the Mean of Order
p (1 ^ p +«=) 300
6.4 Bounded Linear Functionals on iP 304
Problems 310
CHAPTER 7: TOPOLOGICAL SPACES
7.1 Introduction 315
7.2 Open Sets and Closed Sets 317
7.3 Closure—Interior—Boundary 322
7.4 Continuous Functions 326
7.5 Bases 329
7.6 Weak Topologies 333
7.7 Separation 340
7.8 Compactness 344
7.9 Locally Compact Topological Spaces—
Compactification 358
7.10 The Stone Weierstrass Theorem 362
CONTENTS x
7.11 Connectivity 369
Problems 374
CHAPTER 8: BANACH SPACES
8.1 Vector Spaces 386
8.2 Linear Transformations 395
8.3 Linear Functionals—The Hahn Banach
Theorem 400
8.4 The Natural Isomorphism—Reflexive Spaces 409
8.5 The Boundedness of the Inverse Transfor¬
mation 411
8.6 The Closed Graph Theorem—The Uniform
Boundedness Principle 415
8.7 Other Topologies 419
Problems 427
CHAPTER 9: HILBERT SPACE
9.1 Introduction 437
9.2 The Definition and Some Properties 437
9.3 Orthonormal Systems 454
9.4 The Dual Space of a Hilbert Space 468
Problems 472
CHAPTER 10: MEASURE AND INTEGRATION
10.1 Introduction 478
10.2 Measurable Functions and Measure 479
10.3 Integration 486
10.4 Signed Measures 500
10.5 Absolute Continuity 513
10.6 The Lp Spaces 528
10.7 Product Measures and Fubini s Theorem 538
Problems 556
Bibliography 567
Index of Symbols 571
Index 573
|
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| author | Artemiadēs, Nikolaos K. 1917-2010 |
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV006499238 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:47:13Z |
| institution | BVB |
| isbn | 0809307278 |
| language | English |
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| physical | XII, 581 S. |
| publishDate | 1976 |
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| spelling | Artemiadēs, Nikolaos K. 1917-2010 Verfasser (DE-588)135795389 aut Real analysis Carbondale u.a. Southern Ill. Univ. Pr. 1976 XII, 581 S. txt rdacontent n rdamedia nc rdacarrier Fonctions d'une variable réelle ram Fonctions de variables réelles Functions of real variables HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004133288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Artemiadēs, Nikolaos K. 1917-2010 Real analysis Fonctions d'une variable réelle ram Fonctions de variables réelles Functions of real variables |
| title | Real analysis |
| title_auth | Real analysis |
| title_exact_search | Real analysis |
| title_full | Real analysis |
| title_fullStr | Real analysis |
| title_full_unstemmed | Real analysis |
| title_short | Real analysis |
| title_sort | real analysis |
| topic | Fonctions d'une variable réelle ram Fonctions de variables réelles Functions of real variables |
| topic_facet | Fonctions d'une variable réelle Fonctions de variables réelles Functions of real variables |
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