Continuous Linear Representation of Coherent Lower Previsions

This paper studies the possibility of representing lower previsions by continuous linear functionals. We prove the existence of a linear isomorphism between the linear space spanned by the coherent lower previsions and that of an appropriate space of continuous linear functionals. Moreover, we show that a lower prevision is coherent if and only if its transform is monotone. We also discuss the interpretation of these results and the new light they shed on the theory of imprecise probabilities. Keywords coherent lower previsions, M¨obius transform, Choquet’s theorem, Bishop-de Leeuw theorem, Dempster-Shafer-Shapley representation theorem

• Type: Conference
• Year: 2003
• Where: ISIPTA
• Authors: Sebastian Maaß
• Keywords: Coherent Lower Previsions, Continuous Linear Functionals, ISIPTA 2003, Lower Previsions, Mathematics