Let $(\Omega,\Sigma,\mu)$ be a probability space, $E$ be a separable Banach space, $f:\Omega\rightarrow E$ be Borel-measurable and consider the Bochner-integral $$ \bar{\mu}:=\int_{\omega\in \Omega}\, f(\omega)\, \mu(d\omega). $$ If there is a convex set $C\subseteq E$, such that $f(\Omega)$ is a compact subset of $C$ then, is $\bar{\mu}\in C$?