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A minimal 0–1 subshift with noncompact set of ergodic measures
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  • Published: September 1988

A minimal 0–1 subshift with noncompact set of ergodic measures

  • Tomasz Downarowicz1 

Probability Theory and Related Fields volume 79, pages 29–35 (1988)Cite this article

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  • 3 Citations

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Summary

By a minimal 0–1 subshift we mean a pair (X, S), where S denotes the left shift on C={0, 1}z and X is a minimal compact S-invariant subset of C. Developing some of the methods of Williams [2] of obtaining not uniquely ergodic minimal subshifts we construct such a subshift, for which the set of all ergodic measures is noncompact for the weak* topology. In other words, the Choquet simplex of all invariant measures of the subshift is not a Bauer simplex.

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References

  1. Oxtoby, J.C.: Ergodic sets. Bull. Am. Math. Soc. 58, 116–136 (1952)

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  2. Williams, S.: Toeplitz minimal flows which are not uniquely ergodic. Z. Wahrscheinlichkeitstheor. Verw. Geb. 67, 95–107 (1984)

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Wroclaw, Wybrzeze Wyspianskiego 27, PL-50370, Wroclaw, Poland

    Tomasz Downarowicz

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  1. Tomasz Downarowicz
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Downarowicz, T. A minimal 0–1 subshift with noncompact set of ergodic measures. Probab. Th. Rel. Fields 79, 29–35 (1988). https://doi.org/10.1007/BF00319100

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  • Received: 05 May 1986

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319100

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Invariant Measure
  • Left Shift
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