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On the density theorems of Borel und Furstenberg. (English) Zbl 0383.22008


MSC:

22E10 General properties and structure of complex Lie groups
22E15 General properties and structure of real Lie groups
22E40 Discrete subgroups of Lie groups
57S25 Groups acting on specific manifolds
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
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References:

[1] Borel, A., Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math., 72, 179-188 (1960) · Zbl 0094.24901 · doi:10.2307/1970150
[2] Dixmier, J., L’application exponentielle dans les groupes de Lie résolubles, Bull. Soc. Math. France, 85, 113-121 (1957) · Zbl 0077.25203
[3] Furstenberg, H., A note on Borel’s density theorem, Proc. Amer. Math. Soc., 55, 209-212 (1976) · Zbl 0319.22010 · doi:10.2307/2041874
[4] Greenleaf, F.; Moskowitz, M.; Rothschild, L., Unbounded conjugacy classes in Lie groups and the location of central measures, Acta Math., 132, 225-243 (1974) · Zbl 0281.22010 · doi:10.1007/BF02392116
[5] Greenleaf, F.; Moskowitz, M.; Rothschild, L., Compactness of certain homogeneous spaces of finite volume, Amer. J. Math., 97, 248-259 (1975) · Zbl 0296.43009 · doi:10.2307/2373670
[6] Greenleaf, F.; Moskowitz, M.; Rothschild, L., Automorphisms, orbits, and homogeneous spaces of non-connected Lie groups, Math. Ann., 212, 145-155 (1974) · Zbl 0278.22008 · doi:10.1007/BF01350782
[7] Hochschild, G., The structure of Lie groups (1965), San Francisco: Holden-Day, San Francisco · Zbl 0131.02702
[8] Humphreys, J., Linear algebraic groups (1975), Berlin: Springer-Verlag, Berlin · Zbl 0325.20039
[9] Moskowitz, M., Some results on automorphisms of bounded displacement and bounded cocyclesto appear. · Zbl 0391.22004
[10] Mostow, G. D., Factor spaces of solvable groups, Ann. of Math., 60, 1-27 (1954) · Zbl 0057.26103 · doi:10.2307/1969700
[11] Raghunathan, M. S., Discrete subgroups of Lie groups (1972), Berlin: Springer-Verlag, Berlin · Zbl 0254.22005
[12] Saito, M., Sur certains groupes de Lie résolubles, Sci. Papers College Gen. Ed. Univ. Tokyo, 7, 1-11 (1957) · Zbl 0078.01804
[13] Saito, M., Sur certains groupes de Lie résolubles II, Sci. Papers College Gen. Ed. Univ. Tokyo, 7, 157-168 (1957) · Zbl 0079.25701
[14] Wang, S. P., Homogeneous spaces with finite invariant volume, Amer. J. Math., 98, 311-324 (1976) · Zbl 0338.43015 · doi:10.2307/2373886
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