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Jul 6, 2017 at 14:18 comment added Taras Banakh I have red the question more attentively and discovered that I did not answer the question which was posed. The problem was to find a model of ZFC with an ultrafilter (which implies the existence of a translation-invariant measure on each finitely generated abeliang group) but withouts translation-invariant measure on the real line (the construction of such measure requires the existnce of the ultrafilter + the compactness of the circle to the power of continuum).
Jul 6, 2017 at 13:15 history edited Taras Banakh CC BY-SA 3.0
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Jul 6, 2017 at 12:27 history answered Taras Banakh CC BY-SA 3.0