  We consider a super-Brownian motion $X$. Its canonical measures can be
studied through the path-valued process called the Brownian snake. We obtain
the limiting behavior of the volume of the $\epsilon$-neighborhood for the
range of the Brownian snake, and as a consequence we derive the analogous
result for the range of super-Brownian motion and for the support of the
integrated super-Brownian excursion. Then we prove the support of $X_t$ is
capacity-equivalent to $[0,1]^2$ in $\R^d$, $d\geq 3$, and the range of $X$, as
well as the support of the integrated super-Brownian excursion are
capacity-equivalent to $[0,1]^4$ in $\R^d$, $d\geq 5$.
