Solution
= Solution
Project Brownian motion modulo $\mathbb Z^3$ to the compact three-dimensional <torus>. The projected process has normalized volume as invariant probability measure and is irreducible, so it visits every nonempty open set infinitely often almost surely. The image of $S_3$ contains the radius-$\epsilon$ ball about the origin. Hence the original Brownian motion hits $S_3$ at an unbounded set of times.