On entropy and generators of measure-preserving transformations

Krieger, Wolfgang

doi:10.1090/S0002-9947-1970-0259068-3

On entropy and generators of measure-preserving transformations
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by Wolfgang Krieger

Trans. Amer. Math. Soc. 149 (1970), 453-464

DOI: https://doi.org/10.1090/S0002-9947-1970-0259068-3

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Erratum: Trans. Amer. Math. Soc. 168 (1972), 519.

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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