Union-additive multimeasures and self-similarity

In this paper, we study some IFS Markov operators on set-valued mea- sures (multimeasures). Unlike the usual multimeasures in the literature, the multimeasures considered are additive with respect to the union op- eration on sets. This provides an (somewhat unusual) alternative class of multimeasures and it can be considered as an extension of non-additive measures to set-valued measures. After de ning appropriate metrics and proving completeness, we de ne several variations on IFS Markov opera- tors on multimeasures and give many examples