Abstract
Let the group G act on the set X. We will call the set Y a countable section if each Gx n Y is countable. P. Forrest showed in [2] that if a locally compact separable metrizable group G acts freely on a standard measurable space (X, &) with quasi-invariant probability measure ,u, then there is a countable section Y which is in &, and such that the set GY, which is the image of G X Y by a measurable function and therefore p-measurable, has pmeasure 1; in the terminology of [ 11, Y is a complete measurable countable section. We prove the following converse to Forrest’s result:
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