Uniform Endomorphisms Which Are Isomorphic to a Bernoulli Shift
نویسنده
چکیده
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 the past tree of names which is analogous to very weakly Bernoulli or loosely Bernoulli. As a consequence we show that a large class of isometric extensions of the standard example are conjugate to it.
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 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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