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August, 1984 Convergence and Existence of Random Set Distributions
Tommy Norberg
Ann. Probab. 12(3): 726-732 (August, 1984). DOI: 10.1214/aop/1176993223


We study the relation between distributions of random closed sets and their hitting functions $T$, defined by $T(B) = P\{\varphi \cap B \neq \varnothing\}$ for Borel sets $B$. In particular, a sequence of random sets converges in distribution iff the corresponding sequence of hitting functions converges on some sufficiently large class of bounded Borel sets. This class may be chosen to be countable.


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Tommy Norberg. "Convergence and Existence of Random Set Distributions." Ann. Probab. 12 (3) 726 - 732, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0545.60021
MathSciNet: MR744229
Digital Object Identifier: 10.1214/aop/1176993223

Primary: 60D05
Secondary: 60B10 , 60G99

Keywords: alternating set functions , Closed random set , Infinite divisibility , null-arrays , weak convergence

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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