A note on real interpolation of -spaces of vector measures on δ-rings

We describe the real interpolation spaces obtained when we apply the real K-method of Lions–Peetre 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 obtained results are quite different from those in the case of vector measures on σ-algebras described in [9]. However, we find a wide class of vector measures on δ-rings for which the results on σ-algebras hold true.