The Bartle-Dunford-Schwartz integral: integration with respect to a sigma-additive vector measure
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Series: | Monografie Matematyczny
69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 301 S. |
| ISBN: | 9783764386016 3764386010 9783764386023 |
Staff View
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| 100 | 1 | |a Panchapagesan, Thiruvaiyaru V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Bartle-Dunford-Schwartz integral |b integration with respect to a sigma-additive vector measure |c T. V. Panchapagesan |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XV, 301 S. | ||
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Record in the Search Index
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| adam_text | Contents
Preface
ix
1 Preliminaries
1.1 Banach space-valued measures .................... 1
1.2 lcHs-valued measures.......................... 11
2 Basic Properties of the Bartle-Dunford-Schwartz Integral
2.1 (KL) m-integrability.......................... 17
2.2 (BDS) m-integrability......................... 26
3 £p-spaces, 1 p oo
3.1 Theseminormsmp(-,T) on £pM(m), 1 p oo......... 33
3.2 Completeness of £pM(m) and £pI(m), 1 p oo,
and of C00 (m) ............................. 42
3.3 Characterizations of £pI(ra) ,l p oo .............. 47
3.4 Other convergence theorems for £p(m), l p oo......... 54
3.5 Relations between the spaces £p(m)................. 63
4 Integration With Respect to lcHs-valued Measures
4.1 (KL) m-integrability (m lcHs-valued)................. 65
4.2 (BDS) m-integrability (m lcHs-valued)................ 78
4.3 The locally convex spaces jCp.A i(m), £pM(a(V),m),
£pI(m)and £pl(a{P),m), 1 p oo................ 85
4.4 Completeness of £pM(m),£pl(m), CpM((r{V),m)
and £pl(a(V), m), for suitable X................... 91
4.5 Characterizations of £p-spaces, convergence
theorems and relations between £p-spaces..............101
4.6 Separability of £p(m) and £p(a(V), m), 1 p oo,
m lcHs-valued..............................109
viii Contents
5 Applications to Integration in Locally Compact Hausdorff Spaces - Part I
5.1 Generalizations of the Vitali-Carathéodory
Integrability Criterion Theorem.................... 117
5.2 The Baire version of the Dieudonné-Grothendieck
theorem and its vector-valued generalizations............ 121
5.3 Weakly compact bounded Radon operators
and prolongable Radon operators................... 138
6 Applications to Integration in Locally Compact Hausdorff Spaces - Part II
6.1 Generalized Lusin s Theorem and its variants............ 153
6.2 Lusin measurability of functions and sets .............. 159
6.3 Theorems of integrability criteria................... 165
6.4 Additional convergence theorems................... 187
6.5 Duals of £i(m) and C1(Ii)....................... 202
7 Complements to the Thomas Theory
7.1 Integration of complex functions with respect
to a Radon operator.......................... 213
7.2 Integration with respect to a weakly compact
bounded Radon operator........................ 221
7.3 Integration with respect to a prolongable Radon operator..... 233
7.4 Baire versions of Proposition 4.8 and Theorem 4.9 of [T]...... 241
7.5 Weakly compact and prolongable Radon vector measures ..... 251
7.6 Relation between Lv(u) and Cp(mu), u a weakly compact
bounded Radon operator or a prolongable Radon operator..... 275
Bibliography................................... 287
Acknowledgment................................. 293
List of Symbols.................................. 295
Index....................................... 297
|
| adam_txt |
Contents
Preface
ix
1 Preliminaries
1.1 Banach space-valued measures . 1
1.2 lcHs-valued measures. 11
2 Basic Properties of the Bartle-Dunford-Schwartz Integral
2.1 (KL) m-integrability. 17
2.2 (BDS) m-integrability. 26
3 £p-spaces, 1 p oo
3.1 Theseminormsmp(-,T) on £pM(m), 1 p oo. 33
3.2 Completeness of £pM(m) and £pI(m), 1 p oo,
and of C00 (m) . 42
3.3 Characterizations of £pI(ra) ,l p oo . 47
3.4 Other convergence theorems for £p(m), l p oo. 54
3.5 Relations between the spaces £p(m). 63
4 Integration With Respect to lcHs-valued Measures
4.1 (KL) m-integrability (m lcHs-valued). 65
4.2 (BDS) m-integrability (m lcHs-valued). 78
4.3 The locally convex spaces jCp.A'i(m), £pM(a(V),m),
£pI(m)and £pl(a{P),m), 1 p oo. 85
4.4 Completeness of £pM(m),£pl(m), CpM((r{V),m)
and £pl(a(V), m), for suitable X. 91
4.5 Characterizations of £p-spaces, convergence
theorems and relations between £p-spaces.101
4.6 Separability of £p(m) and £p(a(V), m), 1 p oo,
m lcHs-valued.109
viii Contents
5 Applications to Integration in Locally Compact Hausdorff Spaces - Part I
5.1 Generalizations of the Vitali-Carathéodory
Integrability Criterion Theorem. 117
5.2 The Baire version of the Dieudonné-Grothendieck
theorem and its vector-valued generalizations. 121
5.3 Weakly compact bounded Radon operators
and prolongable Radon operators. 138
6 Applications to Integration in Locally Compact Hausdorff Spaces - Part II
6.1 Generalized Lusin's Theorem and its variants. 153
6.2 Lusin measurability of functions and sets . 159
6.3 Theorems of integrability criteria. 165
6.4 Additional convergence theorems. 187
6.5 Duals of £i(m) and C1(Ii). 202
7 Complements to the Thomas Theory
7.1 Integration of complex functions with respect
to a Radon operator. 213
7.2 Integration with respect to a weakly compact
bounded Radon operator. 221
7.3 Integration with respect to a prolongable Radon operator. 233
7.4 Baire versions of Proposition 4.8 and Theorem 4.9 of [T]. 241
7.5 Weakly compact and prolongable Radon vector measures . 251
7.6 Relation between Lv(u) and Cp(mu), u a weakly compact
bounded Radon operator or a prolongable Radon operator. 275
Bibliography. 287
Acknowledgment. 293
List of Symbols. 295
Index. 297 |
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| index_date | 2024-07-02T20:17:01Z |
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| institution | BVB |
| isbn | 9783764386016 3764386010 9783764386023 |
| language | English |
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| physical | XV, 301 S. |
| publishDate | 2008 |
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| publisher | Birkhäuser |
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| series | Monografie Matematyczny |
| series2 | Monografie Matematyczny |
| spelling | Panchapagesan, Thiruvaiyaru V. Verfasser aut The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure T. V. Panchapagesan Basel [u.a.] Birkhäuser 2008 XV, 301 S. txt rdacontent n rdamedia nc rdacarrier Monografie Matematyczny 69 Vector-valued measures Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Vektorwertiges Maß (DE-588)4187472-9 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s Vektorwertiges Maß (DE-588)4187472-9 s DE-604 Monografie Matematyczny 69 (DE-604)BV000003532 69 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Panchapagesan, Thiruvaiyaru V. The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure Monografie Matematyczny Vector-valued measures Integrationstheorie (DE-588)4138369-2 gnd Vektorwertiges Maß (DE-588)4187472-9 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4187472-9 |
| title | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure |
| title_auth | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure |
| title_exact_search | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure |
| title_exact_search_txtP | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure |
| title_full | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure T. V. Panchapagesan |
| title_fullStr | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure T. V. Panchapagesan |
| title_full_unstemmed | The Bartle-Dunford-Schwartz integral integration with respect to a sigma-additive vector measure T. V. Panchapagesan |
| title_short | The Bartle-Dunford-Schwartz integral |
| title_sort | the bartle dunford schwartz integral integration with respect to a sigma additive vector measure |
| title_sub | integration with respect to a sigma-additive vector measure |
| topic | Vector-valued measures Integrationstheorie (DE-588)4138369-2 gnd Vektorwertiges Maß (DE-588)4187472-9 gnd |
| topic_facet | Vector-valued measures Integrationstheorie Vektorwertiges Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003532 |
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