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FOURTH
INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Carnegie Mellon University

Pittsburgh, PA, USA

July 20-23 2005

#
ISIPTA'05 ELECTRONIC PROCEEDINGS

## Serena Doria

# S-Independence and S-Conditional independence with respect to Upper and Lower Conditional Probabilities Assigned by Hausdorff Outer and Inner Measures

### Abstract

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: **

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