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# Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures for Unbounded Random Variables

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications*, PMLR 103:159-166, 2019.

#### Abstract

A model of upper conditional previsions for bounded and unbounded random variables with finite Choquet integral with respect to the Hausdorff outer and inner measures is proposed in a metric space. They are defined by the Choquet integral with respect to Hausdorff outer measures if the conditioning event has positive and finite Hausdorff outer measure in its dimension, otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, they are defined by a 0-1 valued finitely, but not countably, additive probability.