Problem 1451 (difficulty: 5/10)

Let \(\displaystyle \mu\) be a translation-invariant measure on the Borel-sets of \(\displaystyle \R\), for which \(\displaystyle \mu\big([0,1]\big)<\infty\). Show that \(\displaystyle \mu\) is the Lebesgue-measure up to a constant multiple.

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