REMOTAL SETS IN THE SPACE OF P-INTEGRABLE FUNCTIONS

Let X be a Banach space and G be a closed bounded subset of X . For x is an element of X, we set rho( x, G) = sup {parallel to x - y parallel to : y is an element of G}. The set G is called remotal if for any x is an element of X, there exists g is an element of G such that rho(x, G) = parallel to x - g parallel to. In this paper we show that for a separable remotal set G subset of X, the set of p-Bochner integrable functions, L-p (I, G) is in remotal L-p (I, X) : Some other results are presented.