On the estimation of the mean density of random closed sets

Many real phenomena may be modeled as random closed sets in RdRd, of different Hausdorff dimensions. Of particular interest are cases in which their Hausdorff dimension, say nn, is strictly less than dd, such as fiber processes, boundaries of germ–grain models, and nn-facets of random tessellations. A crucial problem is the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous random sets, as defined by the authors in a series of recent papers. While the case n=0n=0 (random vectors, point processes, etc.) has been, and still is, the subject of extensive literature, in this paper we face the general case of any n