Abstract
Abstract 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 card ( G ) {{\rm 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 𝐒 1 {{\bf S}_{1}} .
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