Geodesic
Continuous Ergodic Extensions and Fibre Bundles
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 373-391

Voir la notice de l'article provenant de la source Cambridge University Press

If a locally compact group G acts as a measure preserving transformation group on a Lebesgue space X, then there is a naturally induced unitary representation of G on L2(X), and one can study the action on X by means of this representation. The situation in which the representation has discrete spectrum (i.e., is the direct sum of finite dimensional representations) and the action is ergodic was examined by von Neumann and Halmos when G is the integers or the real line [7], and by Mackey for general non-abelian G [10]. 
Zimmer, Robert J. Continuous Ergodic Extensions and Fibre Bundles. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 373-391. doi: 10.4153/CJM-1978-033-4
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[1] 1. Auslander, L., Green, L. and Hahn, F., Flows on homogeneous spaces, Annals of Math. Studies 53 (1963). Google Scholar

[2] 2. Bredon, G., Introduction to compact transformation groups (Academic Press, New York, 1972). Google Scholar

[3] 3. Ellis, R., Lectures on topological dynamics (Benjamin, New York, 1969). Google Scholar

[4] 4. Furstenberg, H., The structure of distal flows, Amer. J. Math. 85 (1963), 477–515. Google Scholar

[5] 5. Glasner, S., Relatively invariant measures, Pac. J. Math. 58 (1975) 393–410. Google Scholar

[6] 6. Halmos, P. R., Lectures on ergodic theory (Chelsea Pub. Co., New York, 1956). Google Scholar

[7] 7. Halmos, P. R. and von Neumann, J., Operator methods in classical mechanics II, Annals of Math. 43 (1942), 235–247. Google Scholar

[8] 8. Hewitt, E. and Ross, K., Abstract harmonic analysis, Vol. II (Springer-Verlag, Berlin, 1970). Google Scholar

[9] 9. Knapp, A. W., Distal functions on groups, Trans. Amer. Math. Soc. 128 (1967), 1–40. Google Scholar

[10] 10. Mackey, G. W., Ergodic transformation groups with a pure point spectrum, Illinois J. Math. 6 (1962), 327–335. Google Scholar

[11] 11. Zimmer, R. J., Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373–409. Google Scholar

[12] 12. Zimmer, R. J., Ergodic actions with generalized discrete spectrum, Illinois J. Math. 20 (1976), 555–588. Google Scholar

[13] 13. Zimmer, R. J., Distal transformation groups and fibre bundles, Bull. Amer. Math. Soc. 81 (1975), 959–960. Google Scholar

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