2004/11/22 by Christopher Hoffman, Daniel Rudolph · 1 citation
Mathematics · #math.DS #msc:37A35 #msc:28D05 #msc:37A05 #msc:37B10
published as Ann. of Math. (2), Vol. 156 (2002), no. 1, 79--101 · 23 pages, published version
arxiv created 2004/11/22 · arxiv updated 2009/12/01
A \it 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 \it 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 \it very weakly Bernoulli or \it loosely Bernoulli. As a consequence we show that a large class of isometric extensions of the standard example are conjugate to it.