Abstract and Applied Analysis
Volume 2005 (2005), Issue 5, Pages 489-497

On typical Markov operators acting on Borel measures

Tomasz Szarek

Institute of Mathematics, University of Silesia, Bankowa 14, Katowice 40-007, Poland

Received 20 February 2004

Copyright © 2005 Tomasz Szarek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.