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Is it possible to extend the Lebesgue measure as a translation-invariant measure from the Borel sigma-algebra to a sigma-algebra not contained in the Lebesgue sigma-algebra?

user60121
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  • Thanks! It's intereseting though that the only reference given for this problem is an exercise in a single textbook, taking into account how natural this question is, and how non-trivial the construction seems to be. – user60121 Nov 02 '17 at 15:19

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