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On Denjoy-Dunford and Denjoy-Pettis integrals.

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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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