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Israel Journal of Mathematics

, Volume 209, Issue 2, pp 929–948 | Cite as

On infinite transformations with maximal control of ergodic two-fold product powers

  • Terrence M. AdamsEmail author
  • Cesar E. Silva
Article

Abstract

We study the rich behavior of ergodicity and conservativity of Cartesian products of infinite measure-preserving transformations. A class of transformations is constructed such that for any subset R ⊂ ℚ ∩ (0, 1) there exists T in this class such that T p × T q is ergodic if and only if \(\frac{p}{q}\)R. This contrasts with the finite measure-preserving case where T p × T q is ergodic for all nonzero p and q if and only if T × T is ergodic. We also show that our class is rich in the behavior of conservative products.

For each positive integer k, a family of rank-one infinite measure-preserving transformations is constructed which have ergodic index k, but infinite conservative index.

Keywords

Positive Integer Positive Measure Markov Shift Measure Preserve Transformation Conservative Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Department of Defense9161 Sterling Dr.LaurelUSA
  2. 2.Department of Mathematics and StatisticsWilliams CollegeWilliamstownUSA

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