BEPPO-LEVI THEOREM FOR THE VECTOR-VALUED MCSHANE INTEGRAL AND APPLICATIONS

Using only elementary properties of the McShane integral for vector-va lued functions, we establish a convergence theorem which for the scala r case of the integral yields the classical Beppo Levi (monotone) conv ergence theorem as an immediate corollary. As an application, the conv ergence theorem is used to prove that the space of McShane integrable functions, although not usually complete, is ultrabornological.