  In this paper the continuity of the set valued map $p\rightarrow
B_{\Omega,\mathcal{X},p}(r),$ $p\in (1,+\infty),$ is proved where
$B_{\Omega,\mathcal{X},p}(r)$ is the closed ball of the space
$L_{p}\left(\Omega,\Sigma,\mu; \mathcal{X}\right)$ centered at the origin with
radius $r,$ $\left(\Omega,\Sigma,\mu\right)$ is a finite and positive measure
space, $\mathcal{X}$ is separable Banach space. An application to input-output
system described by Urysohn type integral operator is discussed.
