Bernoulli shifts with the same entropy are isomorphic
نویسندگان
چکیده
منابع مشابه
Uniform Endomorphisms Which Are Isomorphic to a Bernoulli Shift
A uniformly p to one endomorphism is a measure preserving map with entropy log p which is a.e. p to 1 and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is one sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite to one endomorphisms conjugate to this standard example by a condition on th...
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A uniformly p-to-one endomorphism is a measure-preserving map with entropy log p which is almost everywhere p-to-one and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is a one-sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by ...
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If Γ is an infinite group with finite symmetric generating set S, we consider the graph G(Γ, S) on [0, 1]Γ by relating two distinct points if an element of s sends one to the other via the shift action. We show that, aside from the cases Γ = Z and Γ = (Z/2Z) ∗ (Z/2Z), G(Γ, S) satisfies a measure-theoretic version of Brooks’ theorem: there is a G(Γ, S)-invariant conull Borel set B ⊆ [0, 1]Γ and ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1970
ISSN: 0001-8708
DOI: 10.1016/0001-8708(70)90029-0