Abstract
Methods of cutting and stacking intervals have been frequently used in ergodic theory to construct transformations with special properties. We show that for independent stacking the partition into subintervals is a Markov partition. In particular, if the resulting transformation is mixing it must be a Bernoulli shift.
Similar content being viewed by others
References
P. Billingsley,Ergodic Theory and Information, John Wiley, New York, 1965.
N. A. Friedman,Introduction to Ergodic Theory, Van Nostrand Reinhold, New York, 1970.
N. A. Friedman, On mixing, entropy and generators,J. Math. Anal. Appl. 26 (1969), 512–528.
N. A. Friedman andD. S. Ornstein, On isomorphism of weak Bernoulli transformations,Advances in Math. 5 (1970), 365–394.
D. S. Ornstein,Imbedding Bernoulli shifts in flows, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1970, pp. 178–218 (Proc. of 1st Midwestern Conference on Ergodic Theory, Ohio State University, Mar. 27–30, 1970).
D. S. Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic,Advances in Math. 5 (1970), 339–348.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shields, P. Cutting and independent stacking of intervals. Math. Systems Theory 7, 1–4 (1973). https://doi.org/10.1007/BF01824799
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01824799