Proximinality in L1(I,X)

Let X bea Banach space and let (I,omega,mu ) bea measurespace . For 1 less than or equivalent p infinity, let Lp(I,X) denotet he spaceof Bochner p-integrable functions defined on I with values in X. The object of this paper is to give sufficient conditions for the proximinality of L1(I,H) + L1(I,G) in L1(I,X), where H and G aret wo proximinal subspaces of X which includea s a special case thep roximality of L1(I)circle time lamba G + H circle time lamba L1(I) in L1(iota plus iota).