On invariants for measure preserving transformations

Fundamenta Mathematicae

Volumn 169, Issue 1, 2001, Pages 51-84

  Hjorth, G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Classification; Measure preserving transformation; Polish group action

Indexed keywords

EID: 0039253706     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: 10.4064/fm169-1-2     Document Type: Article

References (25)

1. H. Becker and A. S. Kechris, The Descriptive Set Theory of Polish Group Actions, London Math. Soc. Lecture Note Ser. 232, Cambridge Univ. Press, Cambridge, 1996.
2. F. Beleznay and M. Foreman, The complexity of the collection of measure distal transformations, Ergodic Theory Dynam. Systems 16 (1996), 929-962.
3. E. Effros, Transformation groups and C*-algebras, Ann. of Math. (2) 81 (1975), 38-55.
4. J. Feldman, Borel structure and invariants for measurable transformations, Proc. Amer. Math. Soc. 46 (1974), 383-394.
5. H. Friedman and L. Stanley, A Borel reducibility theory for classes of structures, J. Symbolic Logic 54 (1989), 894-914.
6. H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, 1981.
7. P. R. Halmos, Measurable transformations, Bull. Amer. Math. Soc. 55 (1949), 1015-1034.
8. _, Recent progress of ergodic theory, ibid. 67 (1961), 70-80.
9. P. R. Halmos and J. von Neumann, Operator methods in classical mechanics II, Ann. of Math. 43 (1942), 332-350.
10. L. A. Harrington, A. S. Kechris and A. Louveau, A Glimm-Effros dichotomy for Borel equivalence relations, J. Amer. Math. Soc. 3 (1990), 903-928.
11. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, 2nd ed., Grundlehren Math. Wiss. 115, Springer, Berlin, 1979.
12. G. Hjorth, Classification and Orbit Equivalence Relations, Math. Surveys Monogr. 75, Amer. Math. Soc., Providence, RI, 2000.
13. G. Hjorth and A. S. Kechris, Borel equivalence relations and classifications by countable models, Ann. Pure Appl. Logic 82 (1996), 221-272.
14. W. Hodges, Model Theory, Cambridge Univ. Press, Cambridge, 1993.
15. A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, Berlin, 1995.
16. S. A. Morris, Pontryagin Duality and the Structure of Locally Compact Abelian Groups, London Math. Soc. Lecture Notes Ser. 29, Cambridge Univ. Press, Cambridge, 1977.
17. Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam, 1980.
18. D. S. Ornstein, Two Bernoulli shifts with the same entropy are isomorphic, Adv. Math. 4 (1970), 337-352.
19. D. S. Ornstein and P. C. Shields, An uncountable family of K-automorphisms, ibid. 10 (1973), 63-88.
20. K. Petersen, Ergodic Theory, Cambridge Univ. Press, Cambridge, 1983.
21. S. Solecki and S. M. Srivastava, Automatic continuity of group operations, Topology Appl. 77 (1997), 65-75.
22. R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 71 (1970). 1-56.
23. B. Weiss, The isomorphism problem in ergodic theory, Bull. Amer. Math. Soc. 78 (1972), 668-684.
24. R. J. Zimmer, Ergodic actions with generalized discrete spectrum, Illinois J. Math. 20 (1976), 373-409.
25. _, Essential Results of Functional Analysis, Univ. of Chicago Press, Chicago, 1990.