REMOTAL SETS IN THE SPACE OF P-INTEGRABLE FUNCTIONS

Abstract. Let X be a Banach space and G be a closed bounded subset of X: For x ϵ X; we set p (x ,G) = sup II x-y II : y ϵ GII: The set G is called remotal if for any x ϵ X; there exists g ϵ G such that p x , G) =II x-gII. In this paper we show that for a separable remotal set G ϵ X, the set of -Bochner integrable functions, L^p(I , G) is in remotal L^p(I , X): Some other results are presented.