Random sets as imprecise random variables

Given a random set coming from the imprecise observation of a random variable, we study how to model the information about the probability distribution of this random variable. Specifically, we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the probabilities induced by the measurable selections; together with sufficient conditions for this, we also give examples showing that they are not equivalent in all cases.