Extreme lower previsions and minkowski indecomposability

  • Authors:

  • Jasper De Bock;Gert de Cooman

  • Affiliations:

  • SYSTeMS Research Group, Ghent University, Zwijnaarde, Belgium;SYSTeMS Research Group, Ghent University, Zwijnaarde, Belgium

  • Venue:
  • ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2013

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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.