  We consider quasisymmetric reparametrizations of the parameter space of the
quadratic family. We prove that the set of quadratic maps which are either
regular or Collet-Eckmann with polynomial recurrence of the critical orbit has
full Lebesgue measure.
  (The intent of this work is just to be a rigorous reference for the companion
preprint Statistical properties of unimodal maps: smooth families with negative
Schwarzian derivative. It is based on the LaTeX file of the paper Statistical
properties of unimodal maps: the quadratic family. The proofs are very similar
and in many places differ just by change of constants.)
