  We compare invariants of N-periodic trajectories in the elliptic billiard,
classic and new, to their aperiodic counterparts via a spatial integrals
evaluated over the boundary of the elliptic billiard. The integrand is weighed
by a universal measure equal to the density of rays hitting a given boundary
point. We find that aperiodic averages are smooth and monotonic on caustic
eccentricity, and perfectly match N-periodic average invariants at the discrete
caustic parameters which admit a given N-periodic family.
