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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On entropy and generators of measure-preserving transformations


Author: Wolfgang Krieger
Journal: Trans. Amer. Math. Soc. 149 (1970), 453-464
MSC: Primary 28.70
Erratum: Trans. Amer. Math. Soc. 168 (1972), 519.
MathSciNet review: 0259068
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Abstract | References | Similar Articles | Additional Information

Abstract: Let T be an ergodic measure-preserving transformation of a Lebesgue measure space with entropy $ h(T)$. We prove that T has a generator of size k where $ {e^{h(T)}} \leqq k \leqq {e^{h(T)}} + 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0259068-3
PII: S 0002-9947(1970)0259068-3
Keywords: Ergodic measure-preserving transformations, entropy, generators of ergodic measure-preserving transformations, shift-invariant measures, coding
Article copyright: © Copyright 1970 American Mathematical Society