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A non-singular dynamical system without maximal ergodic inequality |
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| Authors: | E.H. el Abdalaoui |
| Affiliation: | University of Rouen Normandy, LMRS UMR 60 85 CNRS-UNIV, Departement of Mathematics, Avenue de l''Université, BP.12, 76801 Saint Etienne du Rouvray, France |
| Abstract: | It is shown that there is a non-singular dynamical system for which the maximal ergodic inequality does not hold. We further discuss the connection between a non-singular dynamical systems and the pointwise convergence of the Furstenberg ergodic averages. |
| Keywords: | Ergodic theorems Non-singular maps Furstenberg ergodic averages Birkhoff theorem Strictly ergodic topological model Joining |
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