, Volume 246, Issue 1-2, pp 237-272
Date: 20 Oct 2003

A local Steiner–type formula for general closed sets and applications

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Abstract.

We introduce support (curvature) measures of an arbitrary closed set A in ℝ d and establish a local Steiner–type formula for the localized parallel volume of A. We derive some of the basic properties of these support measures and explore how they are related to the curvature measures available in the literature. Then we use the support measures in analysing contact distributions of stationary random closed sets, with a particular emphasis on the Boolean model with general compact particles.

Mathematics Subject Classification (2000): 53C65, 28A75, 52A22, 60D05; 52A20, 60G57, 60G55, 28A80.