Abstract
Let $\tau$ and $\sigma$ be two commuting ergodic measure preserving transformations of a probablity space, and $\mathrm{Cob}(\tau)$, $\mathrm{Cob}(\sigma)$ be the sets of their coboundaries. We show that the inclusion $\mathrm{Cob}(\sigma) \subseteq \mathrm{Cob}(\tau)$ holds if and only if $\sigma = \tau^{n}$ for some $n \in \mathbb{Z}$. The transformations $\tau$ and $\sigma$ have exactly the same coboundaries if and only if $\sigma = \tau^{\pm1}$. Some related results and open questions are discussed.
Citation
Isaac Kornfeld. "Coboundaries for commuting transformations." Illinois J. Math. 43 (3) 528 - 539, Fall 1999. https://doi.org/10.1215/ijm/1255985108
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