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.
References
Oxtoby, J.C.: Ergodic sets. Bull. Am. Math. Soc. 58, 116–136 (1952)
Williams, S.: Toeplitz minimal flows which are not uniquely ergodic. Z. Wahrscheinlichkeitstheor. Verw. Geb. 67, 95–107 (1984)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00319100
Keywords
- Stochastic Process
- Probability Theory
- Statistical Theory
- Invariant Measure
- Left Shift