  We show that if the density of the absolutely continuous part of a copula is
bounded away from zero on a set of Lebesgue measure 1, then that copula
generates \textquotedblleft lower $\psi$-mixing\textquotedblright\ stationary
Markov chains. This conclusion implies $\phi$-mixing, $\rho$-mixing,
$\beta$-mixing and \textquotedblleft interlaced $\rho$-mixing\textquotedblright
. We also provide some new results on the mixing structure of Markov chains
generated by mixtures of copulas.
