STABILITY OF SOME PROPERTIES OF BANACH-SP ACES

Let Lambda be a Riesz subset in the dual of a compact metrisable abeli an group and let X be a Banach space. We show that the space L(p) (mu, X) has type II-Lambda RNP if and only if X has the same property. If X = Y is a dual space and (Omega, Sigma) is a measure space, then we show that the space M (Omega, X) of X-valued vector measures of bounde d variation has the analytic Radon-Nikodym property if and only if X h as the same property.