On typical Markov operators acting on Borel measures. (English) Zbl 1206.47027
Summary: It is proved that, in the sense of Baire category, almost every Markov operator acting on Borel measures is asymptotically stable and the Hausdorff dimension of its invariant measure is equal to zero.
MSC:
47B38 | Linear operators on function spaces (general) |
28A80 | Fractals |
46E27 | Spaces of measures |
47A35 | Ergodic theory of linear operators |