International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 7, Pages 335-343
doi:10.1155/S0161171204305041
Ergodic sequences of probability measures on commutative hypergroups
Faculty of Mathematics and Computer Science, Bucharest University, Academiei 14, Bucharest 70109, Romania
Received 5 May 2003
Copyright © 2004 Liliana Pavel. 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.
Abstract
We study conditions on a sequence of probability measures {μn}n on a commutative hypergroup K, which ensure that, for any representation π of K on a Hilbert space ℋπ and for any ξ∈ℋπ, (∫Kπx(ξ)dμn(x))n converges to a π-invariant member of ℋπ.