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The nonexistence of certain invariant measures. (English) Zbl 0361.28013
It is proved that on an uncountable group $$G$$ there does not exist a non-zero, $$\sigma$$-finite countably additive measure which is left-invariant and defined on all subsets of $$G$$. There is an earlier proof of this result due to $$F$$. Terpe which, however, as was observed by J. C. Oxtoby, presupposes (a certain consequence of) the continuum hypothesis. The present proof is independent of the continuum hypothesis.
Reviewer: S.G.Dani

MSC:
 28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures 03E10 Ordinal and cardinal numbers 28A25 Integration with respect to measures and other set functions
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