An analogue of the Mostow-Margulis rigidity theorems for ergodic actions of semisimple Lie groups

Author:
Robert J. Zimmer

Journal:
Bull. Amer. Math. Soc. **2** (1980), 168-170

MSC (1970):
Primary 22D40, 22E40, 28A65, 57D30; Secondary 46L10

DOI:
https://doi.org/10.1090/S0273-0979-1980-14706-0

MathSciNet review:
551755

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References | Similar Articles | Additional Information

**1.**A. Connes, J. Feldman, and B. Weiss,*An amenable equivalence relation is generated by a single transformation*, Ergodic Theory Dynamical Systems**1**(1981), no. 4, 431–450 (1982). MR**662736****2.**H. A. Dye,*On groups of measure preserving transformations*. I, Amer. J. Math. 8 (1959), 119-159. MR**131516****3.**G. W. Mackey,*Ergodic theory and virtual groups*, Math. Ann. 166 (1966), 187-207. MR**201562****4.**G. A. Margulis,*Non-uniform lattices in semisimple algebraic groups*, Lie Groups and Their Representations, (ed. I. M. Gelfand), Wiley, New York.**5.**G. A. Margulis,*Discrete groups of motions of manifolds of nonpositive curvature*, Amer. Math. Soc. Trans., vol. 109, 1977, pp. 33-45. MR**492072****6.**G. D. Mostow,*Strong rigidity of locally symmetric spaces*, Ann. of Math. Studies, no. 78, Princeton Univ. Press, Princeton, N. J., 1973. MR**385004****7.**D. Ornstein and B. Weiss (to appear).**8.**R. J. Zimmer,*Amenable ergodic group actions and an application to Poisson boundaries of random walks*, J. Functional Anal. 27 (1978), 350-372. MR**473096****9.**Robert J. Zimmer,*Induced and amenable ergodic actions of Lie groups*, Ann. Sci. École Norm. Sup. (4)**11**(1978), no. 3, 407–428. MR**521638****10.**R. J. Zimmer,*Algebraic topology of ergodic Lie group actions and measurable foliations*(preprint).

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DOI:
https://doi.org/10.1090/S0273-0979-1980-14706-0