On certain spaces of vector measures of bounded variation

If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ℓ∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ℓ∞ in the Bochner space L1(μ,X) and other of the author on the X-inheritance of copies of ℓ∞ in bvca(Σ,X).