Holdings: Real analysis :: THWS Bibkatalog

Real analysis:

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Bibliographic Details
Main Author:	Artemiadēs, Nikolaos K. 1917-2010 (Author)
Format:	Book
Language:	English
Published:	Carbondale u.a. Southern Ill. Univ. Pr. 1976
Subjects:	Fonctions d'une variable réelle Fonctions de variables réelles Functions of real variables
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 581 S.
ISBN:	0809307278

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MARC


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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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indexdate	2024-07-09T16:47:13Z
institution	BVB
isbn	0809307278
language	English
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physical	XII, 581 S.
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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
url	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
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