  We discuss relationships between the McShane, Pettis, Talagrand and Bochner
integrals. A large number of different methods of integration of
Banach-space-valued functions have been introduced, based on the various
possible constructions of the Lebesgue integral. They commonly run fairly
closely together when the range space is separable (or has w^*-separable dual)
and diverge more or less sharply for general range spaces. The McShane integral
as described by [Go] is derived from the `gauge-limit' integral of [McS]. Here
we give both positive and negative results concerning it and the other three
integrals listed above.
