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On Denjoy-Dunford and Denjoy-Pettis integrals

José Gámez, José Mendoza (1998)

Studia Mathematica

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...

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