  This work is devoted to the study of minimal, smooth actions of finitely
generated groups on the circle. We provide a sufficient condition for such an
action to be ergodic (with respect to the Lebesgue measure), and we illustrate
this condition by studying two relevant examples. Under an analogous
hypothesis, we also deal with the problem of the zero Lebesgue measure for
exceptional minimal sets. This hypothesis leads to many other interesting
conclusions, mainly concerning the stationary and conformal measures. Moreover,
several questions are left open. The methods work as well for codimension-one
foliations, though the results for this case are not explicitly stated.
