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The structure of ergodic measures for compact group extensions

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Abstract

In this paper, the structure of the set of invariant measures on a transformation group which is a free compact abelian group extension of another transformation group is studied from both the geometric and analytic viewpoints. It is shown in general that genuine ergodic decompositions are obtained in the non-metric setting for measures that project onto an ergodic measure. In addition, when all the spaces involved are metric, there is a structure theorem for all ergodic measures in terms of the ergodic measures on the base and naturally defined subgroups.

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Authors and Affiliations

  1. University of Sussex, Brighton, England

    H. B. Keynes’ & D. Newton

  2. University of Minnesota, Minneapolis, Minnesota, U.S.A.

    H. B. Keynes’ & D. Newton

Authors
  1. H. B. Keynes’
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  2. D. Newton
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Keynes’, H.B., Newton, D. The structure of ergodic measures for compact group extensions. Israel J. Math. 18, 363–389 (1974). https://doi.org/10.1007/BF02760845

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  • DOI: https://doi.org/10.1007/BF02760845

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