The McShane and the Pettis integral of Banach space-valued functions defined on Rm

In this paper, we define and study the McShane integral of functions mapping a compact interval to I-o in R-m into a Banach space X. We compare this integral with the Pettis integral and prove, in particular, that the two integrals are equivalent if X is reflexive and the unit ball of the dual X* satisfies an additional condition (P). This gives additional information oil an implicitly stated open problem of R.A. Gordon and on the work of D.H. Fremlin and J. Mendoza.