Parry, William; Walters, Peter Endomorphisms of a Lebesgue space. (English) Zbl 0232.28013 Bull. Am. Math. Soc. 78, 272-276 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 11 Documents MSC: 28D05 Measure-preserving transformations 37A99 Ergodic theory × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Donald Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337 – 352. · Zbl 0197.33502 · doi:10.1016/0001-8708(70)90029-0 [2] William Parry, Entropy and generators in ergodic theory, W. A. Benjamin, Inc., New York-Amsterdam, 1969. · Zbl 0175.34001 [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). [4] A. M. Veršik, Descending sequences of measurable decompositions, and their applications, Dokl. Akad. Nauk SSSR 193 (1970), 748 – 751 (Russian). [5] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499 – 530 (Russian). [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). [7] Peter Walters, Roots of \?:1 measure-preserving transformations, J. London Math. Soc. 44 (1969), 7 – 14. · Zbl 0159.07701 · doi: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. · Zbl 0146.28502 · doi:10.1007/BF01692494 [9] Roger Jones and William Parry, Compact abelian group extensions of dynamical systems. II, Compositio Math. 25 (1972), 135 – 147. · Zbl 0243.54039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.