Coherent conditional probabilities, in the sense of de Finetti, are given by a class of Hausdorff dimensional measures. In particular the case where conditioning events have infinite Hausdorff measure is considered. The problem of the exstensions of these conditional probabilities to the class of all subsets of [0,1] is investigated. Conditional upper probabilities, assigned by a class of Hausdorff outer measures, are considered and their properties are analised.
Keywords. coherence, conditional upper probabilities, Hausdorff dimensional outer measures
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