Characterizations of Measurability-Preserving Ergodic Transformations
DOI:
https://doi.org/10.5644/SJM.01.1.06Keywords:
Measurability-preserving ergodic transformations, measurepreserving transformations, ergodic dynamical systems with discrete time and continuous time, weak and strong mixing, Birkhoff ergodic theorem, Hilbert space, unitary operator, Banach space, induced operatorAbstract
Let ($S, \mathfrak{A}, \mu$) be a finite measure space and let $\phi: S \rightarrow S$ be a transformation which preserves the measure $\mu$. The purpose of this paper is to give some (measure theoretical) necessary and sufficient conditions for the transformation $\phi$ to be measurability-preserving ergodic with respect to $\mu$. The obtained results extend well-known results for invertible ergodic transformations and complement the previous work of R.E. Rice on measurability-preserving strong-mixing transformations.
2000 Mathematics Subject Classification. Primary: 28D0
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