  Let $\mu$ be a translation invariant measure on
$(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ and let $\lambda$ denote the
Lebesgue measure on $\mathbb{R}^d$. If there exists an open set $U$ such that
$0<\mu(U)=\lambda(U)<\infty$, it is a simple exercise to show that
$\mu=\lambda|_{\mathcal{B}(\mathbb{R}^d)}$. Is the same conclusion true if $U$
is merely a Borel set?
  The main purpose of this short note is to construct a measure that provides a
negative answer to this question. Incidentally, this construction provides a
new example of a translation invariant measure with a rich domain and range
that is not Hausdorff, a problem previously studied by Hirst.
  Although the constructed measure may exist in the literature, we were unable
to locate any references to it.
