REMOTAL SETS IN ORLICZ SPACES

Let X be a Banach space, (I, mu) be a finite measure space. By L-Phi (I, X), let us denote the space of all X-valued Bochner Orlicz integrable functions on the unit interval I equipped with the Luxemburg norm. A closed bounded subset G of X is called remotal if for any x is an element of X, there exists g is an element of G such that parallel to x - g parallel to = rho (x, G) = sup {parallel to x - y parallel to : y is an element of G}. In this article, we show that for a separable remotal set G subset of X, the set of Bochner integrable functions, L-Phi(I, G) is remotal in L-Phi (I, X). Some other results are presented.