Invariant Measures for Discontinuous Skew-Product Actions of Amenable Semigroups and Some Ergodic Results

Invariant Measures for Discontinuous Skew-Product Actions of Amenable Semigroups and Some Ergodic Results

In this paper, for skew-product actions (SPAs) of amenable semigroups (and commutative semigroups) with discontinuity from the point of view of topology, we establish the Bogolyubov–Krylov theorem for the existence of invariant Borel probability measures. In particular, we obtain uniform and semi-un...

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Veröffentlicht in:Bulletin of the Malaysian Mathematical Sciences Society 2023-05, Vol.46 (3), Article 103
Hauptverfasser: Jafari, Meysam, Sahleh, Abbas, Tootkaboni, Mohammad Akbari
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Discontinuity
Ergodic processes
Existence theorems
Invariants
Mathematics
Mathematics and Statistics
Semigroups
Topology
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Zusammenfassung:In this paper, for skew-product actions (SPAs) of amenable semigroups (and commutative semigroups) with discontinuity from the point of view of topology, we establish the Bogolyubov–Krylov theorem for the existence of invariant Borel probability measures. In particular, we obtain uniform and semi-uniform ergodic theorems for SPAs of amenable semigroups.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01496-0