This paper has two aims. On the one hand, we generalize the notion of sliced measures by means of transversal mappings and study dimensional properties of these measures. On the other hand, as an application of these results, we explain in what sense typical visible parts of a set with large Hausdorff dimension are smaller than the set itself. This is achieved by establishing a connection between dimensional properties of generalized slices and those of visible parts.
"Transversal mappings between manifolds and non-trivial measures on visible parts.." Real Anal. Exchange 30 (2) 675 - 688, 2004-2005.