Abstract
Let φ1, ... ,φ d be commuting measure-preserving transformations, \( \phi ^l \equiv \phi _1^{l_1 } \phi _2^{l_2 } \cdot \cdot \cdot \phi _d^{l_d } ,\Phi = \left\{ {\phi ^l } \right\} \). The Kakutani-Rokhlin tower theorem is proved in a refined form for non-periodic groups Φ, and the Shannon-McMillan theorem is extended to ergodic groups. These results are used to extend recent isomorphism results to groups of transformations.
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Katznelson, Y., Weiss, B. Commuting measure-preserving transformations. Israel J. Math. 12, 161–173 (1972). https://doi.org/10.1007/BF02764660
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DOI: https://doi.org/10.1007/BF02764660