Geodesic
On Denjoy-Dunford and Denjoy-Pettis integrals
Studia Mathematica, Tome 130 (1998) no. 2, pp. 115-133

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $f : [a,b] → c_0$ which is not Pettis integrable on any subinterval in [a,b], while $ʃ_J f$ belongs to $c_0$ 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.
DOI : 10.4064/sm-130-2-115-133

José L. Gámez 1 ; José Mendoza 1

1 
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José L.  Gámez; José Mendoza. On Denjoy-Dunford and Denjoy-Pettis integrals. Studia Mathematica, Tome 130 (1998) no. 2, pp. 115-133. doi: 10.4064/sm-130-2-115-133

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