Strongly Exposed Points of Decomposable Sets in Spaces of Bochner Integrable Functions

A characterization of strongly exposed points of a decomposable bounded closed convex set $\Gamma \subset L_p(T,X)$, where $1\le p<\infty $, in terms of strongly exposed points of values of the set-valued representation $F\ :T\to 2^X$ of $\Gamma$ is given. As a corollary, necessary conditions characterizing strongly exposed points of the unit ball in $L_p(T,X)$, where $1\le p<\infty $, in terms of strongly exposed points of the unit ball in $X$ are obtained.