  The aim of this paper is to present some results about the space L^\Phi(\nu),
where \nu is a vector measure on a compact (not necessarily abelian) group and
\Phi is a Young function. We show that under certain conditions, the space
L^\Phi(\nu) becomes an L^1(G)-module with respect to the usual convolution of
functions. We also define one more convolution structure on L^\Phi(\nu).
