International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 195-198
doi:10.1155/S016117129200022X
Research notes
A note on conservative measures on semigroups
Department of Mathematics, University of Patra, Patra, Greece
Received 6 June 1990
Copyright © 1992 N. A. Tserpes. 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
Consider (S,B,μ) the measure space where S is a topological metric semigroup and μ a countably additive bounded Borel measure. Call μ conservative if all right translations tx:s→sx, x∈S (which are assumed closed mappings) are conservative with respect (S,B,μ) in the ergodic theory sense. It is shown that the semigroup generated by the support of μ is a left group. An extension of this result is obtained for σ-finite μ.