This paper shows the following. (1) is a uniformly non- space if and only if there exist two constants such that, for every 3-dimensional subspace of , there exists a ball-covering of with or which is -off the origin and . (2) If a separable space has the Radon-Nikodym property, then has the ball-covering property. Using this general result, we find sufficient conditions in order that an Orlicz function space has the ball-covering property.
"Ball-Covering Property in Uniformly Non- Banach Spaces and Application." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/873943