Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T23:08:02.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Random set and coverage measure

Published online by Cambridge University Press:  01 July 2016

Guillermo Ayala ,
Juan Ferrandiz  and
Francisco Montes
Guillermo Ayala
Affiliation:
Universitat de València
Juan Ferrandiz
Affiliation:
Universitat de València
Francisco Montes*
Affiliation:
Universitat de València
*
∗Postal address: Departamento de Estadística e Investigación Operativa, Universitat de València, 46100-Burjassot (València), Spain.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known that a random set determines its random coverage measure. The paper gives a necessary and sufficient condition for the reverse implication. An equivalent formulation of the condition constitutes a first step in the search for a way to recognize a random measure as being the random coverage measure of a random set.

Keywords

RANDOM MEASURERANDOM COVERAGE MEASURE
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 972 - 974
Copyright
Copyright © Applied Probability Trust 1991 

Footnotes

This work was supported in part by DGICYT grant no. PB 87-0992.

References

Cruz-Orive, L. M. (1989) Second-order stereology: estimation of reduced second-moment volume measures. Acta Stereol. 8, 641–646.Google Scholar
Jensen, E. B., Kieu, K. and Gundersen, H. J. G. (1990) On the stereological estimation of reduced moment measures. Ann. Inst. Statist. Math. To appear.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Stoyan, D. (1990) Stereology and stochastic geometry. Internat. Statist. Rev. 58, 227–242.Google Scholar
Zähle, M. (1982) Random processes of Hausdorff rectifiable closed sets. Math. Nachr. 108, 49–72.CrossRefGoogle Scholar