Convergence theorems of the Denjoy-Bochner, Denjoy-Pettis and Denjoy-Dunford integrals (Q1300194)
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scientific article; zbMATH DE number 1333207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence theorems of the Denjoy-Bochner, Denjoy-Pettis and Denjoy-Dunford integrals |
scientific article; zbMATH DE number 1333207 |
Statements
Convergence theorems of the Denjoy-Bochner, Denjoy-Pettis and Denjoy-Dunford integrals (English)
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19 July 2000
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The authors prove some convergence theorems for the integrals mentioned in the title of functions taking values in a Banach space \(X\). An additional condition that \(X\) is weakly sequentially complete or the unit ball of the dual \(X^*\) is weak\(^*\) sequentially compact is assumed in some of the convergence theorems.
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Denjoy-Pettis integral
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Denjoy-Dunford integral
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Denjoy-Bochner integral
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functions taking values in a Banach space
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