Holdings: Measure theory and integration

Measure theory and integration:

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Bibliographic Details
Main Author:	Rao, Malempati M. 1929- (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Dekker 2004
Edition:	2. ed., rev. and expanded
Series:	Pure and applied mathematics 265
Subjects:	Intégrales généralisées Mesure, Théorie de la Integrals, Generalized Measure theory Integration > Mathematik Integrationstheorie Maßtheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XIX, 761 S.
ISBN:	0824754018

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MARC


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Record in the Search Index

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adam_text	MEASURE THEORY AND INTEGRATION SECOND EDITION, REVISED AND EXPANDED M. M. RAO UNIVERSITY OF CALIFORNIA, RIVERSIDE RIVERSIDE, CALIFORNIA, U.S.A. MARCEL DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE TO THE SECOND EDITION V PREFACE TO THE FIRST EDITION XI 1. INTRODUCTION AND PRELIMINARIES 1 1.1. MOTIVATION AND OUTLOOK, 1 1.2. THE SPACE W 1 AS A MODEL, 4 1.3. ABSTRACTION OF THE SALIENT FEATURES, 14 2. MEASURABILITY AND MEASURES 21 2.1. MEASURABILITY AND CLASS PROPERTIES, 21 2.2. THE LEBESGUE OUTER MEASURE AND THE CARATHEODORY PROCESS, 30 2.3. EXTENSIONS OF MEASURES TO LARGER CLASSES, 67 2.4. DISTINCTION BETWEEN FINITE AND INFINITE MEASURES, 86 2.5. METRIC OUTER MEASURES, 92 2.6. LEBESGUE-STIELTJES MEASURES, 99 3. MEASURABLE FUNCTIONS 110 3.1. DEFINITION AND BASIC PROPERTIES, 110 3.2. MEASURABILITY WITH MEASURES AND CONVERGENCE, 120 3.3. IMAGE MEASURES AND VAGUE CONVERGENCE, 136 4. CLASSICAL INTEGRATION 147 4.1. THE ABSTRACT LEBESGUE INTEGRAL, 147 4.2. INTEGRATION OF NONMEASURABLE FUNCTIONS, 163 4.3. THE LEBESGUE LIMIT THEOREMS, 171 XVII XVIII CONTENTS 4.4. THE VITALI-HAHN-SAKS THEOREM AND SIGNED MEASURES, 191 4.5. THE L P -SPACES, 203 4.6. THE FOUR BASIC THEOREMS OF BANACH SPACES, 238 5. DIFFERENTIATION AND DUALITY 255 5.1. VARIATIONS OF SET FUNCTIONS AND THE HAHN DECOMPOSITION, 255 5.2. ABSOLUTE CONTINUITY AND COMPLETE MONOTONICITY OF FUNCTIONS, 268 5.3. THE RADON-NIKODYM THEOREM: SIGMA-FINITE CASE, 296 5.4. THE RADON-NIKODYM THEOREM: GENERAL CASE, 320 5.5. DUALITY OF L P -SPACES AND CONDITIONAL EXPECTATIONS, 330 6. PRODUCT MEASURES AND INTEGRALS 364 6.1. BASIC DEFINITIONS AND PROPERTIES, 364 6.2. THE FUBINI-STONE AND TONELLI THEOREMS, 381 6.3. REMARKS ON NON-CARTESIAN PRODUCTS, 398 6.4. INFINITE PRODUCT MEASURES, 405 6.5. TWO APPLICATIONS OF INFINITE PRODUCTS, 437 7. NONABSOLUTE INTEGRATION 452 7.1. NONABSOLUTE INTEGRATION ON THE LINE, 453 7.2. PRODUCT SPACES AND P-INTEGRATION, 488 7.3. VECTOR INTEGRATION, 502 7.4. BOUNDEDNESS PRINCIPLES FOR NONABSOLUTE INTEGRATION, 517 7.5. SOME COMPLEMENTS, 549 8. CAPACITY THEORY AND INTEGRATION 563 8.1. PRELIMINARIES ON ANALYTIC SETS, 563 CONTENTS XIX 8.2. CAPACITY: A CONSTRUCTION AND CHOQUET S THEOREM, 570 8.3. APPLICATION TO THE DANIELL INTEGRAL, 585 9. THE LIFTING THEOREM 599 9.1. THE PROBLEM, MOTIVATION, AND PRELIMINARIES, 599 9.2. EXISTENCE PROOF FOR THE LIFTING MAP, 611 9.3. TOPOLOGIES INDUCED BY LIFTING AND RELATED CONCEPTS, 622 10. TOPOLOGICAL MEASURES 631 10.1. INTRODUCTION AND PRELIMINARIES, 631 10.2. REGULARITY OF MEASURES, 639 10.3. LOCAL FUNCTIONALS AND THE RIESZ-MARKOV THEOREM, 667 10.4. HAAR MEASURES, 687 11. SOME COMPLEMENTS AND APPLICATIONS 703 11.1. LATTICE AND HOMOMORPHISM PROPERTIES, 703 11.2. SOME APPLICATIONS OF THE STONE ISOMORPHISM THEOREM, 713 11.3. REMARKS ON TOPOLOGY OF A GROUP THROUGH MEASURE, 729 APPENDIX 733 REFERENCES 737 INDEX OF SYMBOLS AND NOTATION 747 AUTHOR INDEX 751 SUBJECT INDEX 755
any_adam_object	1
author	Rao, Malempati M. 1929-
author_GND	(DE-588)119519054
author_facet	Rao, Malempati M. 1929-
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author_sort	Rao, Malempati M. 1929-
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bvnumber	BV019833891
callnumber-first	Q - Science
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classification_rvk	SK 430
classification_tum	MAT 280f
ctrlnum	(OCoLC)54505319 (DE-599)BVBBV019833891
dewey-full	515/.42
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515/.42
dewey-search	515/.42
dewey-sort	3515 242
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2. ed., rev. and expanded
format	Book
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indexdate	2024-07-09T20:07:11Z
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isbn	0824754018
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physical	XIX, 761 S.
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publisher	Dekker
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series2	Pure and applied mathematics
spelling	Rao, Malempati M. 1929- Verfasser (DE-588)119519054 aut Measure theory and integration M. M. Rao 2. ed., rev. and expanded New York [u.a.] Dekker 2004 XIX, 761 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 265 Intégrales généralisées Mesure, Théorie de la Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s DE-604 Integration Mathematik (DE-588)4072852-3 s 1\p DE-604 Pure and applied mathematics 265 (DE-604)BV000001885 265 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013158927&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Rao, Malempati M. 1929- Measure theory and integration Pure and applied mathematics Intégrales généralisées Mesure, Théorie de la Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd
subject_GND	(DE-588)4072852-3 (DE-588)4138369-2 (DE-588)4074626-4
title	Measure theory and integration
title_auth	Measure theory and integration
title_exact_search	Measure theory and integration
title_full	Measure theory and integration M. M. Rao
title_fullStr	Measure theory and integration M. M. Rao
title_full_unstemmed	Measure theory and integration M. M. Rao
title_short	Measure theory and integration
title_sort	measure theory and integration
topic	Intégrales généralisées Mesure, Théorie de la Integrals, Generalized Measure theory Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd
topic_facet	Intégrales généralisées Mesure, Théorie de la Integrals, Generalized Measure theory Integration Mathematik Integrationstheorie Maßtheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013158927&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000001885
work_keys_str_mv	AT raomalempatim measuretheoryandintegration

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