On Denjoy-Dunford and Denjoy-Pettis integrals

Tom 130 / 1998

José L. Gámez, José Mendoza Studia Mathematica 130 (1998), 115-133 DOI: 10.4064/sm-130-2-115-133


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.


  • José L. Gámez
  • José Mendoza

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