IDEMPOTENT ULTRAMETRIC FRACTALS

Анотація

The notion of invariant measure is defined for the idempotent measures (Maslov measures) in the ultrametric setting. We prove that the ultrametric space of the idempotent measures on a complete ultrametric space  is also complete and use this fact to prove the existence of the invariant idempotent measure for the IFSs. We also discuss the case of the upper-semicontinuous capacities, of the max-min measures, and also of idempotent measures on metric spaces.