Time changes in flows and mixing

Let $\{U_t\}$ be an ergodic aperiodic flow in a Lebesgue space $(Y,\mu_1)$. By a time change, smooth along the trajectories of the flow and arbitrarily close to the identity, it can be transformed into a mixing flow. If, in addition, $Y$ is a compact metric space, $\{U_t\}$ is continuous and $\mu_1$ is regular, then the change may be chosen to be continuous on and equal to the identity everywhere except on an arbitrary open set of positive measure.