For any σ -finite G-quasiinvariant measure μ given in a G-space, which is G-ergodic and possesses the Steinhaus property, it is shown that every nontrivial countable μ-almost G-invariant partition of the G-space has a μ-nonmeasurable member.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 4, pp. 510–517, April, 2014.
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Kharazishvili, A.B. On Countable Almost Invariant Partitions of G-Spaces. Ukr Math J 66, 572–579 (2014). https://doi.org/10.1007/s11253-014-0954-3
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DOI: https://doi.org/10.1007/s11253-014-0954-3