Convergence theorems for Banach space valued integrable multifunctions
In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω) (1≤p≤∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000516 |
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| _version_ | 1850228400643375104 |
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| author | Nikolaos S. Papageorgiou |
| author_facet | Nikolaos S. Papageorgiou |
| author_sort | Nikolaos S. Papageorgiou |
| collection | DOAJ |
| description | In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω) (1≤p≤∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets. |
| format | Article |
| id | doaj-art-2b59c52303fa4ca88602b148cc327684 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2b59c52303fa4ca88602b148cc3276842025-08-20T02:04:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110343344210.1155/S0161171287000516Convergence theorems for Banach space valued integrable multifunctionsNikolaos S. Papageorgiou0Department of Mathematics, University of California, Davis, California 95616, USAIn this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω) (1≤p≤∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.http://dx.doi.org/10.1155/S0161171287000516convergencemeasurable multifunctionsnonatomic. |
| spellingShingle | Nikolaos S. Papageorgiou Convergence theorems for Banach space valued integrable multifunctions International Journal of Mathematics and Mathematical Sciences convergence measurable multifunctions nonatomic. |
| title | Convergence theorems for Banach space valued integrable multifunctions |
| title_full | Convergence theorems for Banach space valued integrable multifunctions |
| title_fullStr | Convergence theorems for Banach space valued integrable multifunctions |
| title_full_unstemmed | Convergence theorems for Banach space valued integrable multifunctions |
| title_short | Convergence theorems for Banach space valued integrable multifunctions |
| title_sort | convergence theorems for banach space valued integrable multifunctions |
| topic | convergence measurable multifunctions nonatomic. |
| url | http://dx.doi.org/10.1155/S0161171287000516 |
| work_keys_str_mv | AT nikolaosspapageorgiou convergencetheoremsforbanachspacevaluedintegrablemultifunctions |