Complex interpolation of -spaces of vector measures on -rings

We apply the Calderón interpolation methods to Banach lattices of p -integrable and weakly p -integrable functions with respect to a Banach-space-valued measure defined on a δ -ring. In general, the results we obtain are quite different from those in the case of vector measures on σ -algebras. However, we find a wide class of vector measures on δ -rings for which the results on σ -algebras hold true.