A bi-measurable transformation generated by a non-measure preserving transformation (Q2639190)

The author proves a generalization of Rokhlin's extension of a non- invertible measure-preserving transformation to the case of a surjective, nonsingular transformation T: \(X\to X\) [\textit{V. A. Rokhlin}, Izv. Akad. Nauk SSSR, Ser. Mat. 25, 499-530 (1961; Zbl 0107.330)]. This means, there exists a measure on \(Y=\{(y_ n)_{n\geq 0}:\;Ty_{n+1}=y_ n\}\) which projects to the given measure under the first coordinate and the composition operator of S on \(L^ p(Y)\quad (1\leq p<\infty)\) extends isometrically that of T on \(L^ p(X)\).