Special representation of an aperiodic automorphism of a Lebesgue space (Q1916627)

Let \((X,{\mathcal B}, \mu)\) be a Lebesgue probability space. The so-called Rokhlin-Halmos lemma from ergodic theory states that given an aperiodic automorphism \(T\) of \(X\), for every \(n\in N\) and \(\varepsilon>0\) there exists a measurable set \(B\) such that \(\mu(\cup^{n-1}_{j=0} T^jB)>1-\varepsilon\), where the union is meant as a union of disjoint sets. The author defines an \(I\)-configuration, reformulates the above lemma in the new terminology of configurations, and proves that for an aperiodic automorphism \(T\) of a Lebesgue space, there exists an \(I\)-representation of the automorphism for each finite regular configuration \(I\).