Representation theorem for probabilities on IFS-events

Riečan gave in Riečan (2004) [9] an axiomatic characterization of a probability on IFS-events and proved in Riečan (2006) [10] a representation theorem for it. In Renčová [9], Renčová introduced the notions of additive φφ-probability and strongly additive φφ-probability and gave a representation theorem for strongly additive φφ-probabilities.In this paper we give a generalization of the axiomatic characterization given by Riečan in Riečan (2006) [10]; from this, the representation theorem for strongly additive φφ-probabilities will follow.