Best approximation in L p (μ, X ), II

Abstract The object of this paper is to prove the following theorem: If Y is a closed subspace of the Banach space X , then L 1 ( μ , Y ) is proximinal in L 1 ( μ , X ) if and only if L p ( μ , Y ) is proximinal in L p ( μ , Y ) for every p , 1 p Y is either reflexive or Y is a separable proximinal dual space, then L 1 ( μ , Y ) is proximinal in L 1 ( μ , X ).