Complex interpolation of Lp-spaces of vector measures on δ-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 aδ-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.