Endomorphisms of a Lebesgue space

Authors: William Parry and Peter Walters
Journal: Bull. Amer. Math. Soc. 78 (1972), 272-276
MSC (1970): Primary 28A65
DOI: https://doi.org/10.1090/S0002-9904-1972-12954-9
Errata, Volume 78: Bull. Amer. Math. Soc., Volume 78, Number 4 (1972), 628--628
MathSciNet review: 0294604
Full-text PDF Free Access

1. Donald Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337–352. MR 257322, https://doi.org/10.1016/0001-8708(70)90029-0
2. William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0262464
3. A. M. Veršik, A theorem on the lacunary isomorphism of monotonic sequences of partitionings, Funkcional. Anal. i Priložen 2 (1968), no. 3, 17–21 (Russian). MR 0241604
4. A. M. Veršik, Descending sequences of measurable decompositions, and their applications, Dokl. Akad. Nauk SSSR 193 (1970), 748–751 (Russian). MR 0268360
5. V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499–530 (Russian). MR 0143873
6. V. A. Rohlin, Lectures on the entropy theory of transformations with invariant measure, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 3–56 (Russian). MR 0217258
7. Peter Walters, Roots of 𝑛:1 measure-preserving transformations, J. London Math. Soc. 44 (1969), 7–14. MR 232913, https://doi.org/10.1112/jlms/s1-44.1.7
8. Harry Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1–49. MR 0213508, https://doi.org/10.1007/BF01692494
9. Roger Jones and William Parry, Compact abelian group extensions of dynamical systems. II, Compositio Math. 25 (1972), 135–147. MR 338318