Remotal Sets in Orlicz Spaces

Let X be a Banach space, (I, μ) be a finite measure space. By L ^Φ(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 ∈ X, there exists g ∈ G such that ‖x ? g‖ = ρ(x, G) = sup {‖x ? y‖: y ∈ G}. In this article, we show that for a separable remotal set G ? X, the set of Bochner integrable functions, L ^Φ(I, G) is remotal in L ^Φ(I, X). Some other results are presented.