  We prove phase-space mixing for solutions to Liouville's equation for
integrable systems. Under a natural non-harmonicity condition, we obtain weak
convergence of the distribution function with rate $\langle \mathrm{time}
\rangle^{-1}$. In one dimension, we also study the case where this condition
fails at a certain energy, showing that mixing still holds but with a slower
rate. When the condition holds and functions have higher regularity, the rate
can be faster.
