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Quasi-invariant measures on topological groups and \(\omega\)-powers. (English) Zbl 07803149

Summary: Under GCH, there are described the cardinalities of all Hausdorff topological groups \(G\) such that there is a nonzero Borel measure on \(G\) having the \(\mathrm{card}(G)\)-Suslin property and quasi-invariant with respect to an everywhere dense subgroup of \(G\). Some connections are pointed out with the method of Kodaira and Kakutani (1950) for constructing a nonseparable translation invariant extension of the standard Lebesgue (Haar) measure on the circle group \(\mathbf{S}_1\).

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28D05 Measure-preserving transformations
Full Text: DOI

References:

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