Uniform endomorphisms which are isomorphic to a Bernoulli shift

• 成果类型: Article
• 署名作者: Hoffman, C; Rudolph, D
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3597184
• 发表日期: 2002
• 页码: 79-101
• 关键词: entropy

摘要

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 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.