The maximum of branching Brownian motion in ${\mathbb{R}}^d$

We show that in branching Brownian motion (BBM) in ${\mathbb{R}}^d$, $d\ge 2$, the law of $R_t^{\ast }$, the maximum distance of a particle from the origin at time $t$, converges as $t\to \mathrm{\infty }$ to the law of a randomly shifted Gumbel random variable.