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Continuous Ergodic Extensions and Fibre Bundles

Published online by Cambridge University Press:  20 November 2018

Robert J. Zimmer
Robert J. Zimmer*
Affiliation:
United States Naval Academy, Annapolis, Maryland
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 373 - 391
Copyright
Copyright © Canadian Mathematical Society 1978

References

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