Bayesian-like inference, complete disintegrability and complete conglomerability in coherent conditional possibility theory

In this paper we consider Bayesian-like inference processes involving coherent $T$-conditional possibilities assessed on infinite sets of conditional events. For this, a characterization of coherent assessments of possibilistic prior and likelihood is carried on. Since we are working in a finitely maxitive setting, the notions of complete disintegrability and of complete conglomerability are also studied and their relevance in the infinite version of the possibilistic Bayes formula is highlighted.