  R.D.Mauldin asked if every translation invariant $\sigma$-finite Borel
measure on $\RR^d$ is a constant multiple of Lebesgue measure. The aim of this
paper is to show that the answer is "yes and no", since surprisingly the answer
depends on what we mean by Borel measure and by constant. We present Mauldin's
proof of what he called a folklore result, stating that if the measure is only
defined for Borel sets then the answer is affirmative. Then we show that if the
measure is defined on a $\sigma$-algebra \emph{containing} the Borel sets then
the answer is negative. However, if we allow the multiplicative constant to be
infinity, then the answer is affirmative in this case as well. Moreover, our
construction also shows that an isometry invariant $\sigma$-finite Borel
measure (in the wider sense) on $\RR^d$ can be non-$\sigma$-finite when we
restrict it to the Borel sets.
