Disintegration property of coherent upper conditional previsions with respect to Hausdorff outer measures for unbounded random variables

Abstract

In a metric space , coherent upper conditional previsions are defined by Hausdorff outer measures on the linear space of all absolutely Choquet integrable random variables. They are proven to satisfy the disintegration property on every non-null partition if Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension. Coherent upper conditional probabilities are obtained as restrictions to the indicators function and it is proven they can be extended as finitely additive probabilities in the sense of Dubins. Examples are given in the discrete metric space and in the Euclidean metric space.