Abstract
Under the Continuum Hypothesis, it is proved that any nonzero $\sigma$-finite metrically transitive invariant measure on a group of cardinality continuum admits a nonseparable invariant extension. An application of this result to the left Haar measure on a $\sigma$-compact locally compact topological group of the same cardinality is also presented.
Citation
A. B. Kharazishvili. "METRICAL TRANSITIVITY AND NONSEPARABLE EXTENSIONS OF INVARIANT MEASURES." Taiwanese J. Math. 13 (3) 943 - 949, 2009. https://doi.org/10.11650/twjm/1500405449
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