  Let $W(t)$, $0\leq t\leq T$, be a Brownian motion in $\mathbb{R}^d$, $d=2,3$.
We say that $x$ is a cut point for $W$ if $x=W(t)$ for some $t\in(0,T)$ such
that $W [0,t) $ and $W (t,T]$ are disjoint. In this work, we prove that a.s.
the Minkowski content of the set of cut points for $W$ exists and is finite and
non-trivial.
