Representation theorem for probabilities on IFS-events

Riečan gave in Riečan (2004) an axiomatic characterization of a probability on IFS-events and proved in Riečan (2006) a representation theorem for it. In Renčová , Renčová introduced the notions of additive image-probability and strongly additive image-probability and gave a representation theorem for strongly additive image-probabilities. In this paper we give a generalization of the axiomatic characterization given by Riečan in Riečan (2006) ; from this, the representation theorem for strongly additive image-probabilities will follow.