Mathematische Zeitschrift

, Volume 246, Issue 1, pp 237–272

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


DOI: 10.1007/s00209-003-0597-9

Cite this article as:
Hug, D., Last, G. & Weil, W. Math. Z. (2004) 246: 237. doi:10.1007/s00209-003-0597-9


We introduce support (curvature) measures of an arbitrary closed set A in ℝd 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburg i. Br.Germany
  2. 2.Institut für Mathematische StochastikUniversität Karlsruhe (TH)KarlsruheGermany
  3. 3.Mathematisches Institut IIUniversität Karlsruhe (TH)KarlsruheGermany

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