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 L 1 ( μ , X ) and other of the author on the X-inheritance of copies of ℓ ∞ in bvca ( Σ , X ) .