Serena Doria

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Upper and lower conditional probabilities are defined by Hausdorff outer and inner measures, when the conditioning events have positive and finite Hausdorff outer and inner measures in their dimension, otherwise, when the conditioning events have Hausdorff outer or inner measure equal to zero or infinity in their dimension, they are defined by a 0–1 valued(More)
A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure(More)
In this paper the notion of s-irrelevance with respect to upper and lower conditional probabilities assigned by Hausdorff outer and inner measures is proved to be a sufficient condition for strong independence introduced for credal sets. An example is given to show that the converse is not true. Moreover the definition of sconditional irrelevance is given(More)
Let (Ω, d) be a metric space and let B be a partition of Ω. For every set B of B with positive and finite Hausdorff outer measure in its Hausdorff dimension, a coherent conditional measure of risk is defined as the Choquet integral with respect to Hausdorff outer measure. Two risks are defined to be s-independent if the atoms of the classes generated by(More)
Let (Ω, d) be a metric space where Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension and let B be a partition of Ω. The coherent upper conditional prevision defined as the Choquet integral with respect to its associated Hausdorff outer measure is proven to satisfy the disintegration property and the conglomerative(More)