  For any given Wulff shape $\mathcal{W}$, we can define the unique continuous
function $S^{n}\to \mathbb{R}_{+}$ called convex integrand, denoted by
$\gamma_{{}_{\mathcal{W}}}$. In this paper, we show that, for any Wulff shapes
$\mathcal{W}_{1}$ and $\mathcal{W}_{2}$, the equality
$d(\gamma_{{}_{\mathcal{W}_{1}}}, \gamma_{{}_{\mathcal{W}_{2}}})=
h(\mathcal{W}_{1}, \mathcal{W}_{2})$ holds, where $d$ is the maximum distance
of the function space consisting of convex integrands and $h$ is the
Pompeiu-Hausdorff distance of the space consisting of Wulff shapes. Moreover,
applications of this result are given.
