A random set in a space E is defined, in agreement with the usual approach of axiomatic probability, as a set-valued random variable, that is, as a measurable map from some abstract probability space into a system of subsets of E, endowed with a suitable σ-algebra. It has turned out to be particularly tractable to assume that E is a locally compact space with a countable base and to consider the system F of its closed subsets, equipped with the topology of closed convergence and the induced σ-algebra of Borel sets. This approach is described in Section 2.1.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Random Closed Sets. In: Stochastic and Integral Geometry. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78859-1_2
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DOI: https://doi.org/10.1007/978-3-540-78859-1_2
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