Vector measures:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1998
|
| Ausgabe: | reprint. |
| Schriftenreihe: | Mathematical surveys
15 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 277 - 310 |
| Beschreibung: | XIII, 322 S. |
| ISBN: | 9780821815151 0821815156 |
Internformat
MARC
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| 100 | 1 | |a Diestel, Joseph |d 1943- |e Verfasser |0 (DE-588)108479773 |4 aut | |
| 245 | 1 | 0 | |a Vector measures |c by J. Diestel and J. J. Uhl |
| 250 | |a reprint. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1998 | |
| 300 | |a XIII, 322 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys |v 15 | |
| 500 | |a Literaturverz. S. 277 - 310 | ||
| 650 | 0 | 7 | |a Vektorwertiges Maß |0 (DE-588)4187472-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Uhl, John J. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematical surveys |v 15 |w (DE-604)BV001888016 |9 15 | |
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Datensatz im Suchindex
| _version_ | 1804145580886196224 |
|---|---|
| adam_text | CONTENTS
Foreword
............................................................
v
Introduction
.........................................................ix
I. General vector measure theory
...................................1
1.
Elementary properties of vector measures
.....................1
2.
Countably additive vector measures
.........................10
3.
The
Nikodým Boundedness
Theorem
........................14
4.
Rosenthal s lemma and the structure of a
vector measure
................................................18
5.
The
Carathéodory-Hahn-Kluvanek
Extension Theorem
and strongly additive vector measures
............................25
6.
Notes and remarks
........................................31
II. Integration
...................................................41
1.
Measurable functions
......................................41
2.
The Bochner integral
......................................44
3.
The Pettis integral
........................................52
4.
An elementary version of the
Bartle
integral
..................56
5.
Notes and remarks
........................................57
III. Analytic
Radon-Nikodým
theorems and operators on
Li(ß).........59
1.
The
Radon-Nikodým
theorem and Riesz representable
operators on L (p)
.............................................59
2.
Representable operators, weak compactness and
Radon-Nikodým
theorems
......................................67
3.
Separable dual spaces and the
Radon-Nikodým
Property
.......79
4.
Notes and remarks
........................................83
IV. Applications of analytic
Radon-Nikodým
theorems
................97
1.
The dual of Lfa, X)
......................................97
2.
Weakly compact subsets of
Ц(џ,
X)
........................101
3.
Gel fand spaces
..........................................106
4.
Integral operators on
Lp(ß) ...............................107
5.
The Lewis-Stegall theorem with a dash of Pelczynski
.........113
vii
viii CONTENTS
6.
Notes and remarks
.......................................115
V. Martingales
..................................................121
1.
Conditional expectations and martingales
...................121
2.
Convergence theorems
....................................125
3.
Dentable sets and the
Radon-Nikodým
property
.............131
4.
The
Radon-Nikodým
property for
Ĺ
/μ,
X)
.................140
5.
Notes and remarks
.......................................141
VI. Operators on spaces of continuous functions
.....................147
1.
Operators on
Β(Σ)
and
¿„(μ)
.............................148
2.
Weakly compact operators on
C(Û)
and the Riesz
Representation Theorem
.......................................151
3.
Absolutely summing operators on C(Q)
.....................161
4.
Nuclear operators on C(Q)
................................169
5.
Notes and remarks
.......................................176
VII.
Geometric aspects of the
Radon-Nikodým
property
...............187
1.
The
Kreïn-Mil man
theorem and the
Radon-Nikodým
property
.....................................................187
2.
Separable dual spaces, the
Kreïn-Mil man
property and
the
Radon-Nikodým
property
..................................191
3.
Strongly exposed points and the
Radon-Nikodým
property
....................................................199
4.
The
Radon-Nikodým
property and the existence of extreme
points for nonconvex closed bounded sets
.......................203
5.
Notes and remarks
.......................................208
6.
Summary of equivalent formulations of the
Radon-
Nikodým
property
............................................217
7.
The
Radon-Nikodým
property for specific spaces
............218
VIII.
Tensor products of Banach spaces
..............................221
1.
The least and greatest crossnorms
..........................221
2.
The duals of X®
Y
and X <g>
Y
...........................229
3.
The approximation and metric approximation properties
......238
4.
Applications of tensor products and vector measures to
Banach space theory
..........................................245
5.
Notes and remarks
.......................................253
IX. The range of a vector measure
.................................261
1.
The Liapounoff Convexity Theorem
........................261
2.
Rybakov s theorem
.......................................267
3.
Extreme point phenomena
................................269
4.
Notes and remarks
.......................................272
Bibliography
........................................................277
Subject index
.....................................................311
Author index
.....................................................319
|
| any_adam_object | 1 |
| author | Diestel, Joseph 1943- Uhl, John J. |
| author_GND | (DE-588)108479773 |
| author_facet | Diestel, Joseph 1943- Uhl, John J. |
| author_role | aut aut |
| author_sort | Diestel, Joseph 1943- |
| author_variant | j d jd j j u jj jju |
| building | Verbundindex |
| bvnumber | BV037307105 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)246248790 (DE-599)BVBBV037307105 |
| discipline | Mathematik |
| edition | reprint. |
| format | Book |
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| genre | Vektor-Maß gnd |
| genre_facet | Vektor-Maß |
| id | DE-604.BV037307105 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:21:43Z |
| institution | BVB |
| isbn | 9780821815151 0821815156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022461635 |
| oclc_num | 246248790 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-83 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-83 DE-188 |
| physical | XIII, 322 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys |
| series2 | Mathematical surveys |
| spelling | Diestel, Joseph 1943- Verfasser (DE-588)108479773 aut Vector measures by J. Diestel and J. J. Uhl reprint. Providence, RI American Math. Soc. 1998 XIII, 322 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys 15 Literaturverz. S. 277 - 310 Vektorwertiges Maß (DE-588)4187472-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Vektor-Maß gnd rswk-swf Vektorwertiges Maß (DE-588)4187472-9 s Banach-Raum (DE-588)4004402-6 s DE-604 Vektor-Maß f Uhl, John J. Verfasser aut Mathematical surveys 15 (DE-604)BV001888016 15 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022461635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diestel, Joseph 1943- Uhl, John J. Vector measures Mathematical surveys Vektorwertiges Maß (DE-588)4187472-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4187472-9 (DE-588)4004402-6 |
| title | Vector measures |
| title_auth | Vector measures |
| title_exact_search | Vector measures |
| title_full | Vector measures by J. Diestel and J. J. Uhl |
| title_fullStr | Vector measures by J. Diestel and J. J. Uhl |
| title_full_unstemmed | Vector measures by J. Diestel and J. J. Uhl |
| title_short | Vector measures |
| title_sort | vector measures |
| topic | Vektorwertiges Maß (DE-588)4187472-9 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Vektorwertiges Maß Banach-Raum Vektor-Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022461635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001888016 |
| work_keys_str_mv | AT diesteljoseph vectormeasures AT uhljohnj vectormeasures |