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Bibliographic Details
Main Author:	Bichteler, Klaus 1938- (Author)
Format:	Book
Language:	English
Published:	Basel [u.a.] Birkhäuser 1998
Series:	Birkhäuser advanced texts
Subjects:	Integrals Measure theory Integrationstheorie Integration > Mathematik Maßtheorie Lebesgue-Integral Riemannsches Integral
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	VIII, 193 S.
ISBN:	3764359366 0817659366

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adam_text	Contents Preface vii Chapter I Review 1 1.1 Introduction 1 1.2 Notation 3 1.3 The Theorem of Stone Weierstrafi 8 1.4 The Riemann Integral 17 1.5 An Integrability Criterion 21 1.6 The Permanence Properties 23 1.7 Seminorms 28 Chapter II Extension of the Integral 31 II. 1 E additivity 33 11.2 Elementary Integrals 35 11.3 The Daniell Mean 42 11.4 Negligible Functions and Sets 48 11.5 Integrable Functions 52 11.6 Extending the Integral 58 11.7 Integrable Sets 61 11.8 Example of a Non Integrable Function 66 Chapter III Measurability 69 111.1 Littlewood s Principles 70 111.2 The Permanence Properties 73 111.3 The Integrability Criterion 75 111.4 Measurable Sets 81 111.5 Baire and Borel Functions 85 111.6 Further Properties of Daniell s Mean 92 111.7 The Procedures of Lebesgue and Carathedory 95 vi Chapter IV The Classical Banach Spaces 101 IV.1 The p norms 102 IV.2 The CP spaces 105 IV.3 The LP spaces 108 IV.4 Linear Functionals 112 IV.5 The Dual of LP 118 IV.6 The Hilbert space L2 122 Chapter V Operations on Measures 125 V.I Products of Elementary Integrals 125 V.2 The Theorems of Fubini and Tonelli 130 V.3 An Application: Convolution 133 V.4 An Application: Marcinkiewicz Interpolation 134 V.5 Signed Measures 137 V.6 The Space of Measures 144 V.7 Measures with Densitites 151 V.8 The Radon Nikodym Theorem 154 V.9 An Application: Conditional Expectation 155 V.10 Differentiation 157 Appendix A Answers to Selected Problems 165 References 180 Index of Notations 181 Index 184
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indexdate	2024-12-20T10:19:57Z
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isbn	3764359366 0817659366
language	English
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physical	VIII, 193 S.
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spellingShingle	Bichteler, Klaus 1938- Integration - a functional approach Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd
subject_GND	(DE-588)4138369-2 (DE-588)4072852-3 (DE-588)4074626-4 (DE-588)4034949-4 (DE-588)4049996-0
title	Integration - a functional approach
title_auth	Integration - a functional approach
title_exact_search	Integration - a functional approach
title_full	Integration - a functional approach Klaus Bichteler
title_fullStr	Integration - a functional approach Klaus Bichteler
title_full_unstemmed	Integration - a functional approach Klaus Bichteler
title_short	Integration - a functional approach
title_sort	integration a functional approach
topic	Integrals Measure theory Integrationstheorie (DE-588)4138369-2 gnd Integration Mathematik (DE-588)4072852-3 gnd Maßtheorie (DE-588)4074626-4 gnd Lebesgue-Integral (DE-588)4034949-4 gnd Riemannsches Integral (DE-588)4049996-0 gnd
topic_facet	Integrals Measure theory Integrationstheorie Integration Mathematik Maßtheorie Lebesgue-Integral Riemannsches Integral
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008003466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bichtelerklaus integrationafunctionalapproach

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