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Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers

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Abstract

LetS be a nonlacunary subsemigroup of the natural numbers and letμ be anS-invariant and ergodic measure. Using entropy arguments on a symbolic representation of the inverse limit of this action, we show that if any element inS has positive entropy with respect toμ, thenμ is Lebesgue.

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Authors and Affiliations

  1. Department of Mathematics, Tufts University, 02155, Medford, MA, USA

    Aimee S. A. Johnson

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  1. Aimee S. A. Johnson
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Johnson, A.S.A. Measures on the circle invariant under multiplication by a nonlacunary subsemigroup of the integers. Israel J. Math. 77, 211–240 (1992). https://doi.org/10.1007/BF02808018

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  • DOI: https://doi.org/10.1007/BF02808018

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