Stefan-M.~Heinemann, Oliver Schmitt
Rokhlin's Lemma for Non-Invertible Maps
Preprint series: Mathematica Gottingensis

MSC:

28C10 Set functions and measures on topological groups, Haar measures, invariant measures

Abstract: We present an elementary proof of Rokhlin's Lemma for measurable endomorphisms
of separable spaces which are aperiodic with respect to an invariant Borel
probability measure. As an application we explicitely compute the Rokhlin
sets for classes of interval maps and Bernoulli shifts.

Keywords: Measurable Endomorphism, Invariant Measure, Symbolic Dynamics