Independence with Respect to Upper and Lower Conditional Probabilities Assigned by Hausdorff Outer and Inner Measures

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 Ω=[0,1] of finitely additive conditional probabilities, in the sense of Dubins, assigned by a class of Hausdorff measures. A weak disintegration property is introduced when conditional probability is defined by a class of Hausdorff dimensional measures. Moreover the definition of s-independence and s-irrelevance are given to assure that logical indepedence 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

• Type: Conference
• Year: 2003
• Where: ISIPTA
• Authors: Serena Doria
• Keywords: Conditional Probabilities, Hausdorff Measures, ISIPTA 2003, Lower Conditional Probabilities, Mathematics