Abstract
Coherent lower previsions constitute a convex set that is closed and compact under the topology of point-wise convergence, and Maaß [2] has shown that any coherent lower prevision can be written as a ‘countably additive convex combination’ of the extreme points of this set. We show that when the possibility space has a finite number n of elements, these extreme points are either degenerate precise probabilities, or in a one-to-one correspondence with the (Minkowski) indecomposable compact convex subsets of ℝn − 1.
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De Bock, J., de Cooman, G. (2013). Extreme Lower Previsions and Minkowski Indecomposability. In: van der Gaag, L.C. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2013. Lecture Notes in Computer Science(), vol 7958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39091-3_14
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DOI: https://doi.org/10.1007/978-3-642-39091-3_14
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