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 s-conditional irrelevance is given and a generalized factorization property is proposed as necessary condition of s-conditional irrelevance. An example is given to show that s-conditional irrelevance and s-irrelevance are not related; moreover sufficient conditions are given for equivalence between s-conditional irrelevance and s-irrelevance. Finally the notion of s-irrelevance is extended to random variables.
Keywords. Independence, strong independence, conditional independence, Hausdorff outer and inner measures
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Authors addresses:
Department of Earth Sciences
Universita'G.D'Annunzio
Via dei Vestini 31
66013 Chieti
Italy
E-mail addresses:
| Serena Doria | s.doria@dst.unich.it |