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Normal ergodic actions and extensions

Research paper by R. C. Fabec

Indexed on: 01 Jun '81Published on: 01 Jun '81Published in: Israel Journal of Mathematics



Abstract

We demonstrate that normal ergodic extensions of group actions are characterized as skew product actions given by cocycles into locally compact groups. As a consequence, Robert Zimmer’s characterization of normal ergodic group actions is generalized to the noninvariant case. We also obtain the uniqueness theorem which generalizes the von Neumann Halmos uniqueness theorem and Zimmer’s uniqueness theorem for normal actions with relative discrete spectrum.