Curvature measures and random sets. II
type: Item
instance of: scholarly article
title: Curvature measures and random sets. II
zbMATH Open document ID: 0554.60017
DOI: 10.1007/BF00366271
author: Martina Zähle
publication date: 1986-01-01T00:00:00Z
review text: [For part I see Math. Nachr. 119, 327-339 (1984; Zbl 0553.60014).] In choosing models of stochastic geometry three general problems play a role which are closely connected with each other: 1. Construction of the random geometric objects under consideration; 2. Measurabilities; 3. Geometric behaviour. In the present paper second order local geometric properties of random subsets of \(R^ d\) are of interest. These properties are described by signed curvature measures in a measure geometric context. The theory of point processes on general spaces (here on the space of subsets with positive reach) provides an appropriate framework for solving construction and measurability problems. Mean value relations for random curvature measures associated with such set processes are derived by means of invariance properties. Ergodic interpretations of the curvature densities are also given. The appendix provides auxiliary results for random signed Radon measures in locally compact separable Hausdorff spaces.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 3883297
zbMATH Keywords: models of stochastic geometry
zbMATH Keywords: signed curvature measures
zbMATH Keywords: ergodic interpretations
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00366271
OpenAlex ID: W1975005096
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 3883297