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${\bi T},{\bi T}^{\bf -1}$ is not standard

Published online by Cambridge University Press:  01 August 1998

DEBORAH HEICKLEN  and
CHRISTOPHER HOFFMAN
DEBORAH HEICKLEN
Affiliation:
Mathematics Department, University of California, Berkeley, CA 94720, USA (e-mail: heicklen@math.berkeley.edu)
CHRISTOPHER HOFFMAN
Affiliation:
Mathematics Department, University of Maryland, College Park, MD 20742, USA (email: hoffman@math.umd.edu)
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Abstract

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A sequence of random variables, $Y_0,Y_1,Y_2,\ldots\,$, is called standard if there exists a one-sided isomorphism between it and a sequence of independent random variables. In this paper it is demonstrated that the sequence arising from the past of the $T,T^{-1}$ map is not standard.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 4 , August 1998 , pp. 875 - 878
Copyright
© 1998 Cambridge University Press