Advanced integration theory:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1998
|
| Series: | Mathematics and its applications
454 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 861 S. |
| ISBN: | 0792352343 |
Staff View
MARC
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| 245 | 1 | 0 | |a Advanced integration theory |c by Corneliu Constantinescu ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1998 | |
| 300 | |a IX, 861 S. | ||
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| 490 | 1 | |a Mathematics and its applications |v 454 | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 4 | |a Exercice analyse | |
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| 650 | 7 | |a Mesure, Théorie de la |2 ram | |
| 650 | 4 | |a Théorème recouvrement Vitali | |
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 4 | |a Measure theory | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Preface vii
Acknowledgements x
Introduction 1
Suggestions to the Reader 5
0 Preliminaries 7
1 Vector Lattices 21
1.1 Ordered Vector Spaces 21
1.2 Vector Lattices 38
1.3 Substructures, Quotients, Products 58
1.4 Bands and Orthogonality 79
1.5 Homomorphisms 95
1.6 The Order Dual of a Vector Lattice 126
1.7 Continuous Functionals 142
1.8 Order and Topology 167
1.9 Metric Spaces and Banach Spaces 197
1.10 Banach Lattices 236
1.11 Hilbert Lattices 260
1.12 Lattice Products 272
2 Elementary Integration Theory 279
2.1 Riesz Lattices 279
2.2 Daniell Spaces 293
2.3 The Closure of a Daniell Space 308
2.4 The Integral for a Daniell Space 330
2.5 Systems of Sets, Step Functions, and Stone Lattices 340
2.6 Positive Measures 352
2.7 Closure, Completion, and Integrals for Positive Measure Spaces . . 371
2.8 Measurable Spaces and Measurability 386
2.9 Measurability versus Integrability 393
2.10 Stieltjes Functionals and Stieltjes Measures. Lebesgue Measure . . 416
vi Table of Contents
3 LP Spaces 447
3.1 Classes modulo^ and Convergence in Measure 447
3.2 The Holder and Minkowski Inequalities and the £P Spaces 466
3.3 // Spaces for 0 p °° 490
3.4 Uniform integrability and the Generalized Lebesgue Convergence
Theorem 506
3.5 Localization 524
3.6 Products and L°° 542
4 Real Measures 549
4.1 Nullcontinuous Functionals 549
4.2 Real Measures and Spaces of Real Measures 559
4.3 Integrals for Real Measures 578
4.4 Bounded Measures 608
4.5 Atomic and Atomless Measures 619
5 The Radon Nikodym Theorem. Duality 637
5.1 Absolute Continuity 637
5.2 The Theorem of Radon Nikodym 656
5.3 Duality for Function Spaces 663
6 The Classical Theory of Real Functions 681
6.1 Functions of Locally Finite Variation 681
6.2 Real Stieltjes Measures 711
6.3 Absolutely Continuous Functions 724
6.4 Vitali s Covering Theorem 736
6.5 Differentiate Functions 760
6.6 Spaces of Multiply Differentiable Functions 781
6.7 Riemann Stieltjes Integrals 792
Historical Remarks 805
Name Index 808
Subject Index 810
Symbol Index 849
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| id | DE-604.BV012447786 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:27:45Z |
| institution | BVB |
| isbn | 0792352343 |
| language | English |
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| physical | IX, 861 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Advanced integration theory by Corneliu Constantinescu ... Dordrecht [u.a.] Kluwer Acad. Publ. 1998 IX, 861 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 454 Analyse fonctionnelle ram Exercice analyse Intégrales généralisées ram Mesure, Théorie de la ram Théorème recouvrement Vitali Integrals, Generalized Measure theory Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Constantinescu, Corneliu Sonstige oth Mathematics and its applications 454 (DE-604)BV008163334 454 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008447015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Advanced integration theory Mathematics and its applications Analyse fonctionnelle ram Exercice analyse Intégrales généralisées ram Mesure, Théorie de la ram Théorème recouvrement Vitali Integrals, Generalized Measure theory Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4138369-2 |
| title | Advanced integration theory |
| title_auth | Advanced integration theory |
| title_exact_search | Advanced integration theory |
| title_full | Advanced integration theory by Corneliu Constantinescu ... |
| title_fullStr | Advanced integration theory by Corneliu Constantinescu ... |
| title_full_unstemmed | Advanced integration theory by Corneliu Constantinescu ... |
| title_short | Advanced integration theory |
| title_sort | advanced integration theory |
| topic | Analyse fonctionnelle ram Exercice analyse Intégrales généralisées ram Mesure, Théorie de la ram Théorème recouvrement Vitali Integrals, Generalized Measure theory Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Analyse fonctionnelle Exercice analyse Intégrales généralisées Mesure, Théorie de la Théorème recouvrement Vitali Integrals, Generalized Measure theory Integrationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008447015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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