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Bibliographic Details
Main Authors:	Filter, Wolfgang (Author), Weber, Karl (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Chapman & Hall 1997
Edition:	1. ed.
Series:	Chapman & Hall mathematics series
Subjects:	Functions of real variables Integrals, Generalized Measure theory Integration > Mathematik Integrationstheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743172&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XII, 294 S.
ISBN:	0412576805

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Record in the Search Index

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adam_text	Titel: Integration theory Autor: Filter, Wolfgang Jahr: 1997 Contents Preface vii Introduction ix 1 Preliminaries 1 2 Function spaces and functionals 9 2.1 Ordered sets and lattices 9 2.2 The spaces K x and ffi* 17 2.3 Vector lattices of functions 23 2.4 Functionals 30 2.5 Daniell spaces 46 3 Extension of Danieli spaces 49 3.1 Upper functions 50 3.2 Lower functions 53 3.3 The closure of ( X , Â£, Â£) 55 3.4 Convergence theorems for ( X, Â£(Â£), i) 62 3.5 Examples 69 3.6 Null functions, null sets and integrability 75 3.7 Examples 86 3.8 The induction principle 88 3.9 Functionals on K x 91 3.10 Summary 98 4 Measure and integral 101 4.1 Extensions of positive measure spaces 102 4.2 Examples 120 4.3 Locally integrable functions 124 vi Contents 4.4 ^-measurable functions 128 4.5 Product measures and Fubiniâ€™s theorem 139 5 Measures on Hausdorff spaces 159 5.1 Regular measures 159 5.2 Measures on metric and locally compact spaces 176 5.3 The congruence invariance of the n-dimensional Lebesgue measure 188 6 Â£ p -spaces 195 6.1 The structure of Â£ p -spaces 195 6.2 Uniform integrability 209 7 Vector lattices, Â£ p -spaces 221 7.1 Vector lattices 221 7.2 L p -spaces 235 8 Spaces of measures 241 8.1 The vector lattice structure and Hahnâ€™s theorem 241 8.2 Absolute continuity and the Radon-Nikodym theorem 255 9 Elements of the theory of real-valued functions on R 263 9.1 Functions of locally finite variation 263 9.2 Absolutely continuous functions 268 Symbol index 283 Subject index 287
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illustrated	Not Illustrated
indexdate	2024-12-20T10:13:47Z
institution	BVB
isbn	0412576805
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-007743172
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physical	XII, 294 S.
publishDate	1997
publishDateSearch	1997
publishDateSort	1997
publisher	Chapman & Hall
record_format	marc
series2	Chapman & Hall mathematics series
spellingShingle	Filter, Wolfgang Weber, Karl Integration theory Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd
subject_GND	(DE-588)4072852-3 (DE-588)4138369-2
title	Integration theory
title_auth	Integration theory
title_exact_search	Integration theory
title_full	Integration theory W. Filter and K. Weber
title_fullStr	Integration theory W. Filter and K. Weber
title_full_unstemmed	Integration theory W. Filter and K. Weber
title_short	Integration theory
title_sort	integration theory
topic	Functions of real variables Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd
topic_facet	Functions of real variables Integrals, Generalized Measure theory Integration Mathematik Integrationstheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743172&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT filterwolfgang integrationtheory AT weberkarl integrationtheory

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