STABILITY OF SOME PROPERTIES OF BANACH-SPACES

Let Lambda be a Riesz subset in the dual of a compact metrisable abelian 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 bounded variation has the analytic Radon-Nikodym property if and only if X has the same property.