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* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to 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-Dundord and Denjoy-Pettis integrals are studied.
@article{bwmeta1.element.bwnjournal-article-smv130i2p115bwm,
author = {Jos\'e G\'amez and Jos\'e Mendoza},
title = {On Denjoy-Dunford and Denjoy-Pettis integrals},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {115-133},
zbl = {0971.28009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i2p115bwm}
}
Gámez, José; Mendoza, José. On Denjoy-Dunford and Denjoy-Pettis integrals. Studia Mathematica, Tome 129 (1998) pp. 115-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i2p115bwm/
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