1
12. 6. 2024.
Characterizations of Measurability-Preserving Ergodic Transformations
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