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Joint ergodicity along generalized linear functions
Published online by Cambridge University Press: 15 June 2015
Abstract
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A criterion of joint ergodicity of several sequences of transformations of a probability measure space 
$X$ of the form 
$T_{i}^{\unicode[STIX]{x1D711}_{i}(n)}$ is given for the case where 
$T_{i}$ are commuting measure-preserving transformations of 
$X$ and 
$\unicode[STIX]{x1D711}_{i}$ are integer-valued generalized linear functions, that is, the functions formed from conventional linear functions by an iterated use of addition, multiplication by constants, and the greatest integer function. We also establish a similar criterion for joint ergodicity of families of transformations depending on a continuous parameter, as well as a condition of joint ergodicity of sequences 
$T_{i}^{\unicode[STIX]{x1D711}_{i}(n)}$ along primes.
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