Measure theory and integration:
Saved in:
| Main 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: | |
| Links: | 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 |
| Physical Description: | XIX, 761 S. |
| ISBN: | 0824754018 |
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| 245 | 1 | 0 | |a Measure theory and integration |c M. M. Rao |
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Record in the Search Index
| _version_ | 1819369379534471168 |
|---|---|
| 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- |
| author_role | aut |
| author_sort | Rao, Malempati M. 1929- |
| author_variant | m m r mm mmr |
| building | Verbundindex |
| bvnumber | BV019833891 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312 |
| callnumber-search | QA312 |
| callnumber-sort | QA 3312 |
| callnumber-subject | QA - Mathematics |
| 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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| id | DE-604.BV019833891 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T12:06:52Z |
| institution | BVB |
| isbn | 0824754018 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013158927 |
| oclc_num | 54505319 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-11 |
| owner_facet | DE-824 DE-703 DE-11 |
| physical | XIX, 761 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| 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 |