The elements of integration and Lebesgue measure:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York ; Chichester ; Brisbane ; Toronto ; Singapore
Wiley
1995
|
| Ausgabe: | Wiley Classics Library Edition |
| Schriftenreihe: | Wiley classics library
A Wiley-interscience publication |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007224458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | x, 179 Seiten |
| ISBN: | 0471042226 9780471042228 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819332341051424768 |
|---|---|
| adam_text | THE ELEMENTS OF INTEGRATION AND LEBESGUE MEASURE ROBERT G. BARTLE
EASTERN MICHIGAN UNIVERSITY AND UNIVERSITY OF ILLINOIS WILEY CLASSICS
LIBRARY EDITION PUBLISHED 1995 A WILEY-INTERSCIENCE PUBLICATION JOHN
WILEY & SONS, INC. NEW YORK * CHICHESTER * BRISBANE * TORONTO *
SINGAPORE R CONTENTS THE ELEMENTS OF INTEGRATION 1. INTRODUCTION 1
REASONS FOR THE DEVELOPMENT OF THE LEBESGUE INTEGRAL, COMPARISON WITH
THE RIEMANN INTEGRAL, THE EXTENDED REAL NUMBER SYSTEM 2. MEASURABLE
FUNCTIONS 6 MEASURABLE SETS AND FUNCTIONS, COMBINATIONS, COMPLEX- VALUED
FUNCTIONS, FUNCTIONS BETWEEN MEASURABLE SPACES 3. MEASURES 19 MEASURES,
MEASURE SPACES, ALMOST EVERYWHERE, CHARGES 4. THE INTEGRAL 27 SIMPLE
FUNCTIONS AND THEIR INTEGRALS, THE INTEGRAL OF A NON- NEGATIVE EXTENDED
REAL-VALUED MEASURABLE FUNCTION, THE MONOTONE CONVERGENCE THEOREM,
FATOU S LEMMA, PROP- ERTIES OF THE INTEGRAL VN VIII CONTENTS 5.
INTEGRABLE FUNCTIONS INTEGRABLE REAL-VALUED FUNCTIONS, POSITIVITY AND
LINEARITY OF THE INTEGRAL, THE LEBESGUE DOMINATED CONVERGENCE THEOREM,
INTEGRANDS THAT DEPEND ON A PARAMETER 41 6. THE LEBESGUE SPACES L P
NORMED LINEAR SPACES, THE L P SPACES, HOLDER S INEQUALITY, MINKOWSKI S
INEQUALITY, THE COMPLETENESS THEOREM, THE SPACE LQO 52 7. MODES OF
CONVERGENCE RELATIONS BETWEEN CONVERGENCE IN MEAN, UNIFORM CON-
VERGENCE, ALMOST EVERYWHERE CONVERGENCE, CONVERGENCE IN MEASURE, AND
ALMOST UNIFORM CONVERGENCE, EGOROFF S THE- OREM, THE VITALI CONVERGENCE
THEOREM 65 8. DECOMPOSITION OF MEASURES 80 HAHN AND JORDAN DECOMPOSITION
THEOREMS, THE RADON- NIKODYM THEOREM, LEBESGUE DECOMPOSITION THEOREM,
THE RIESZ REPRESENTATION THEOREM FOR L P 9. GENERATION OF MEASURES 96
MEASURES ON ALGEBRAS OF SETS, THE EXTENSION OF MEASURES, CARATHE ODORY
AND HAHN EXTENSION THEOREMS, LEBESGUE AND LEBESGUE-STIELTJES MEASURE,
THE RIESZ REPRESENTATION THEOREM FOR C 10. PRODUCT MEASURES RECTANGLES,
THE PRODUCT MEASURE THEOREM, SECTIONS, THE MONOTONE CLASS LEMMA, TONELLI
AND FUBINI THEOREMS 113 CONTENTS IX THE ELEMENTS OF LEBESGUE MEASURE 11.
VOLUMES OF CELLS AND INTERVALS 127 CELLS, INTERVALS, LENGTH, CELLS IN R
P , P-DIMENSIONAL VOLUME, TRANSLATION INVARIANCE 12. THE OUTER MEASURE
131 THE OUTER MEASURE IN JR P , PROPERTIES OF M*, TRANSLATION INVARIANCE
13. MEASURABLE SETS 139 A-ALGEBRAS, MEASURE ON A CONDITION,
CARATH&XIORY S THEOREM, LEBESGUE SETS AND LEBESGUE MEASURE, UNIQUENESS
OF LEBESGUE MEASURE, SOME USEFUL PROPERTIES 14. EXAMPLES OF MEASURABLE
SETS 149 BOREL SETS, NULL SETS, TRANSLATION INVARIANCE, EXISTENCE OF
NON-BOREL SETS 15. APPROXIMATION OF MEASURABLE SETS 155 APPROXIMATION BY
OPEN SETS, APPROXIMATION BY CLOSED SETS, APPROXIMATION BY COMPACT SETS,
APPROXIMATION BY CELLS 16. ADDITIVITY AND NONADDITIVITY 161 ADDITIVITY,
CARATHE ODORY REVISITED, INNER MEASURE CONTENTS 17. NONMEASURABLE AND
NON-BOREL SETS 165 THE DIFFERENCE SET, RATIONAL EQUIVALENCE, VITALI S
SET, NON- ADDITIVE DECOMPOSITIONS, AN UBIQUITOUS SET, A SINGULAR
FUNCTION, EXISTENCE OF NON-BOREL SETS REFERENCES 175 INDEX 177
|
| any_adam_object | 1 |
| author | Bartle, Robert G. 1927-2003 |
| author_GND | (DE-588)13732877X |
| author_facet | Bartle, Robert G. 1927-2003 |
| author_role | aut |
| author_sort | Bartle, Robert G. 1927-2003 |
| author_variant | r g b rg rgb |
| building | Verbundindex |
| bvnumber | BV010812627 |
| 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 |
| ctrlnum | (OCoLC)33666831 (DE-599)BVBBV010812627 |
| dewey-full | 515.43 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.43 |
| dewey-search | 515.43 |
| dewey-sort | 3515.43 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Wiley Classics Library Edition |
| format | Book |
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| id | DE-604.BV010812627 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:01:12Z |
| institution | BVB |
| isbn | 0471042226 9780471042228 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007224458 |
| oclc_num | 33666831 |
| open_access_boolean | |
| owner | DE-824 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-824 DE-19 DE-BY-UBM DE-11 |
| physical | x, 179 Seiten |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley classics library A Wiley-interscience publication |
| spellingShingle | Bartle, Robert G. 1927-2003 The elements of integration and Lebesgue measure Integral calculus Integraalrekening gtt Integrationstheorie swd Lebesgue-Maß swd Maattheorie gtt Maßtheorie swd Integrals, Generalized Measure theory |
| title | The elements of integration and Lebesgue measure |
| title_auth | The elements of integration and Lebesgue measure |
| title_exact_search | The elements of integration and Lebesgue measure |
| title_full | The elements of integration and Lebesgue measure Robert G. Bartle, Esatern Michigan University and University of Illinois |
| title_fullStr | The elements of integration and Lebesgue measure Robert G. Bartle, Esatern Michigan University and University of Illinois |
| title_full_unstemmed | The elements of integration and Lebesgue measure Robert G. Bartle, Esatern Michigan University and University of Illinois |
| title_short | The elements of integration and Lebesgue measure |
| title_sort | the elements of integration and lebesgue measure |
| topic | Integral calculus Integraalrekening gtt Integrationstheorie swd Lebesgue-Maß swd Maattheorie gtt Maßtheorie swd Integrals, Generalized Measure theory |
| topic_facet | Integral calculus Integraalrekening Integrationstheorie Lebesgue-Maß Maattheorie Maßtheorie Integrals, Generalized Measure theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007224458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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