  Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$,
of different Hausdorff dimensions. In many real applications, such as fiber
processes and $n$-facets of random tessellations of dimension $n\leq d$ in
spaces of dimension $d\geq1$, several problems are related to the estimation of
such mean densities. In order to confront such problems in the general setting
of spatially inhomogeneous processes, we suggest and analyze an approximation
of mean densities for sufficiently regular random closed sets. We show how some
known results in literature follow as particular cases. A series of examples
throughout the paper are provided to illustrate various relevant situations.
