Decomposable sets and Musielak-Orlicz spaces of multifunctions
Volume 68 / 2005
Banach Center Publications 68 (2005), 71-77
MSC: 46E30, 46E99, 28B20.
DOI: 10.4064/bc68-0-8
Abstract
We introduce the Musielak-Orlicz space of multifunctions $X_{m,\varphi }$ and the set $S^{\varphi }_{F}$ of $\varphi $-integrable selections of $F$. We show that some decomposable sets in Musielak-Orlicz space belong to $X_{m,\varphi }$. We generalize Theorem 3.1 from [6]. Also, we get some theorems on the space $X_{m,\varphi }$ and the set $S^{\varphi }_{F}$.
