References
Blattner, R., Automorphic group representations.Pacific J. Math., 8 (1958), 665–677.
Connes, A., Une classification des facteurs de type III.Ann. Sci. École Norm. Sup., 6 (1973), 133–252.
— Almost periodic states and factors of type III1.J. Functional Analysis, 186 (1974), 415–445.
— Outer conjugacy classes of automorphisms of factors.Ann. École Norm. Sup., 8 (1975), 383–419.
— Classification of injective factors, cases II1, II∞, IIIλ, λ≠1.Ann. of Math., 104 (1976), 73–115.
— On the classification of von Neumann algebras and their automorphisms.Symposia Math., 20 (1976), 435–478.
— Periodic automorphisms of the hyperfinite factor of type II1.Acta Sci. Math., 39 (1977), 39–66.
— Sur la théorie noncommutative de l’intégration.Lecture Notes in Math., Springer-Verlag, 725 (1979), 19–143.
Connes, A., Feldman, J. &Weiss, B., Amenable equivalence relations are hyperfinite.J. Ergodic Theory and Dynamics, 1 (1981), 431–450.
Connes, A. &Takesaki, M., The flow of weights on factors of type III.Tôhoku Math., J., 29 (1977), 473–575; Errata.
Dye, H., On groups of measure preserving transformations, I.Amer. J. Math., 81 (1959), 119–159; II,ibid. Amer. J. Math., 85 (1963), 551–576.
Feldman, J. &Moore, C. C., Ergodic equivalence relations, cohomology, and von Neumann algebras, I.Trans Amer. Math. Soc., 234 (1977), 289–324; II,ibid. Trans. Amer. Math. Soc., 234 (1977), 325–359.
Huebschmann, J., Dissertation, E.T.H. 5999, Zürich, 1977.
Jones, V., Actions of finite groups on the hyperfinite type II1 factor.Mem. Amer. Math. Soc., 237 (1980).
— An invariant for group actions, algèbres d’opérateurs.Lecture Notes in Math., Springer-Verlag, 725 (1979), 237–253.
Jones, V. Prime actions of compact abelian groups on the hyperfinite II1 factor. To appear.
Katayama, Y., Non-existence of a normal conditional expectation in a continuous crossed product.Kodai Math. J., 4 (1981), 345–352.
Feldman, J. &Lind, D., Hyperfiniteness and the Halmos-Rohlin theorem for nonsingular abelian actions.Proc. Amer. Math. Soc., 55 (1976), 339–344.
Krieger, W., On ergodic flows and the isomorphism of factors.Math. Ann., 223 (1976), 19–70.
Mackey, G. W., Ergodic theory and virtual groups.Math. Ann., 166 (1966), 187–207.
McDuff, D., Central sequences and the hyperfinite factor.Proc. London Math. Soc., 21 (1970), 443–461.
Nakamura, M. &Takeda, Z., On certain examples of the crossed product of finite factors, I.Proc. Japan Acad., 34 (1958), 495–499; II.ibid.Proc. Japan Acad., 500–502.
Ocneanu, A., Actions of discrete amenable groups on factors. To appear.
Olesen, D., Pedersen, G. K. &Takesaki, M., Ergodic actions of compact abelian groups.J. Operator theory, 3 (1980), 237–269.
Schmidt, K.,Lectures on cocycles for ergodic group actions. Univ. Warwick Lecture Notes Series.
Sutherland, C.,Notes on orbit equivalence: Krieger’s theorem. Lecture Notes Series No. 23, Oslo (1976).
Suzuki, N., A linear representation of a countable infinite group.Proc. Japan Acad., 34 (1958), 575–579.
Takesaki, M., Duality for crossed products and the structure of von Neumann algebras of type III.Acta Math. 131 (1973), 249–310.
Habegger, N., Jones, V., Pino-Ortiz, O., Ratcliffe, J., Relative cohomology of groups.Comm. Math. Helv., 59 (1994), 149–164.
Ornstein, D., On the root problem in ergodic theory.Proc. Sixth Berkeley Symposium on Math. Statistic and Prob., Vol. 3 1972).
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This research was supported in part by NSF Grant no. MCS79-03041.
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Jones, V.F.R., Takesaki, M. Actions of compact abelian groups on semifinite injective factors. Acta Math. 153, 213–258 (1984). https://doi.org/10.1007/BF02392378
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DOI: https://doi.org/10.1007/BF02392378