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.