Commuting measure-preserving transformations

Yitzhak Katznelson; Benjamin Weiss

doi:10.1007/BF02764660

Commuting measure-preserving transformations

Yitzhak Katznelson^*
, Benjamin Weiss

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

87 Scopus citations

Abstract

Let φ₁, ...,φ_d be commuting measure-preserving transformations, {Mathematical expression}. 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.

Original language	English
Pages (from-to)	161-173
Number of pages	13
Journal	Israel Journal of Mathematics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/BF02764660
State	Published - Jun 1972

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title = "Commuting measure-preserving transformations",

abstract = "Let φ1, ...,φ d be commuting measure-preserving transformations, \{Mathematical expression\}. 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.",

author = "Yitzhak Katznelson and Benjamin Weiss",

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AB - Let φ1, ...,φ d be commuting measure-preserving transformations, {Mathematical expression}. 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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Commuting measure-preserving transformations

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