ON DENJOY-DUNFORD AND DENJOY-PETTIS INTEGRALS

The two main results of this paper are the following: (a) If X is a Ba nach space and f : [a, b] --> X is a function such that xf is Denjoy integrable for all x is an element of X*, then f is Denjoy-Dunford in tegrable, 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. Gordo n in [4]. Some other questions in connection with Denjoy-Dunford and D enjoy-Pettis integrals are studied.