Upper and lower conditional probabilities assigned by Hausdorff outer and inner measures are given; they are natural extensions to the class of all subsets of omega=[0,1] of finitely additive probabilities, in the sense of Dubins, assigned by a class of Hausdorff measures. A strong disintegration property is introduced when conditional probability is defined by a class of Hausdorff dimensional measures. Moreover the definitions of s-independence and s-irrelevance are given to assure that logical independence is a necessary condition of independence. The interpretation of commensurable events, in the sense of de Finetti, as sets with finite and positive Hausdorff measure and with the same Hausdorff dimension is proposed.
Keywords. Upper and lower conditional probabilities, Hausdorff measures, disintegration property, independence.
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Universita'G.D'Annunzio
Via dei Vestini 31
66013 Chieti
Italy
E-mail addresses:
| Serena Doria | s.doria@dst.unich.it |