Representation theorem for probabilities on IFS-events

Authors:
Lavinia Corina Ciungu;Beloslav Riečan
Affiliations:
Polytechnical University of Bucharest Splaiul Independenei 113, Bucharest, Romania and State University of New York - Buffalo, 244 Mathematics Building, Buffalo, NY 14260-2900, USA;Matej Bel University, Tajovského 40, SK-97401 Banská Bystrica, Slovak Republic and Mathematical Institute of Slovak Acad. of Sciences, Štefánikova 49, SK-81473 Bratislava, Slov ...
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

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