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On Denjoy-Dunford and Denjoy-Pettis integrals.


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

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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.

Tipo de documento:Artículo
Palabras clave:Banach-valued functions; Denjoy-Dunford integrals; Denjoy-Pettis integrals
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:15426

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