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Gámez Merino, José Luis and Mendoza Casas, José
(1998)
*On Denjoy-Dunford and Denjoy-Pettis integrals.*
Studia Mathematica, 130
(2).
pp. 115-133.
ISSN 0039-3223

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## Abstract

The two main results of this paper are the following: (a) If X is a Banach space and f : [a, b] --> X is a function such that x*f is Denjoy integrable for all x* is an element of X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function f : [a, b] --> c(0) which is not Pettis integrable on any subinterval in [a, b], while integral(J)f belongs to co for every subinterval J in [a, b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dunford and Denjoy-Pettis integrals are studied.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Banach-valued functions; Denjoy-Dunford integrals; Denjoy-Pettis integrals |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 15426 |

Deposited On: | 30 May 2012 08:07 |

Last Modified: | 25 Jun 2018 07:37 |

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