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


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.


Positive Integer Positive Measure Markov Shift Measure Preserve Transformation Conservative Index 
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© 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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