  Let $(\xi(s))_{s\geq 0}$ be a standard Brownian motion in $d\geq 1$
dimensions and let $(D_s)_{s \geq 0}$ be a collection of open sets in $\R^d$.
For each $s$, let $B_s$ be a ball centered at 0 with $\vol(B_s) = \vol(D_s)$.
We show that $\E[\vol(\cup_{s \leq t}(\xi(s) + D_s))] \geq \E[\vol(\cup_{s \leq
t}(\xi(s) + B_s))]$, for all $t$. In particular, this implies that the expected
volume of the Wiener sausage increases when a drift is added to the Brownian
motion.
