This paper investigates the concepts of irrelevance and independence in connection with imprecise probability models. We study the general properties of Walley's concepts of epistemic irrelevance and epistemic independence and their relation to the graphoid axioms. Simple examples are given to show that epistemic irrelevance can violate the symmetry, contraction and intersection axioms, that epistemic independence can violate contraction and intersection, and that this accords with the intuitive notions of irrelevance and independence.
Keywords. Sets of probability measures, lower expectations, graphoid axioms, independence concepts.
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