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A short proof of the Ornstein theorem

Published online by Cambridge University Press:  14 June 2011

T. DOWNAROWICZ  and
J. SERAFIN
T. DOWNAROWICZ
Affiliation:
Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland (email: downar@pwr.wroc.pl, serafin@pwr.wroc.pl)
J. SERAFIN
Affiliation:
Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland (email: downar@pwr.wroc.pl, serafin@pwr.wroc.pl)
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Abstract

We give a short (and fairly elementary) proof of the ‘residual Sinai theorem’ of which the Ornstein theorem is an immediate consequence. In principle, we follow the lines of [BKS] but our proof avoids any substantial quotations, in particular, invoking any characterizations of systems isomorphic to Bernoulli shifts. The core of the proof is five pages long and it relies only on standard facts in ergodic theory.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 587 - 597
Copyright
Copyright © Cambridge University Press 2011

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References

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