Upper and lower conditional probabilities induced by a multivalued mapping
Given a (finitely additive) full conditional probability space and a conditional measurable space , a multivalued mapping Γ from X to Y induces a class of full conditional probabilities on . A closed form expression for the lower and upper envelopes ⁎ and ⁎ of such class is provided: the envelopes can be expressed through a generalized Bayesian conditioning rule, relying on two linearly ordered classes of (possibly unbounded) inner and outer measures.