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On $v$-positive type transformations in infinite measure

Volume 140 / 2015

Tudor Pădurariu, Cesar E. Silva, Evangelie Zachos Colloquium Mathematicum 140 (2015), 149-170 MSC: Primary 37A40. DOI: 10.4064/cm140-2-1


For each vector $v$ we define the notion of a $v$-positive type for infinite-measure-preserving transformations, a refinement of positive type as introduced by Hajian and Kakutani. We prove that a positive type transformation need not be $(1,2)$-positive type. We study this notion in the context of Markov shifts and multiple recurrence, and give several examples.


  • Tudor PădurariuUniversity of California
    Los Angeles, CA 90095-1555, U.S.A.
  • Cesar E. SilvaDepartment of Mathematics
    Williams College
    Williamstown, MA 01267, U.S.A.
  • Evangelie ZachosPrinceton University
    Princeton, NJ 08544, U.S.A.

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