The Annals of Probability

Locally Finite Random Sets: Foundations for Point Process Theory

B. D. Ripley

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Abstract

The foundations of point process theory are surveyed. An abstract theory motivated by applications in stochastic geometry is presented. It is shown that it is sufficient to know only which sets are measurable and which are bounded in the basic space, where we use countability hypotheses rather than topological assumptions. (The sole exception is in the construction of probabilities where pseudo-topological hypotheses are needed.) It is shown that there are close connections with the random set theories of Kendall and Matheron.

Article information

Source
Ann. Probab., Volume 4, Number 6 (1976), 983-994.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995941

Digital Object Identifier
doi:10.1214/aop/1176995941

Mathematical Reviews number (MathSciNet)
MR474478

Zentralblatt MATH identifier
0359.60066

JSTOR
links.jstor.org

Subjects
Primary: 60G05: Foundations of stochastic processes
Secondary: 60B99: None of the above, but in this section

Keywords
Random sets point processes avoidance functions bounded spaces

Citation

Ripley, B. D. Locally Finite Random Sets: Foundations for Point Process Theory. Ann. Probab. 4 (1976), no. 6, 983--994. doi:10.1214/aop/1176995941. https://projecteuclid.org/euclid.aop/1176995941


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