Abstract: In this paper we shall show that there exists L_0 such that for each even integer L >= L_0
there exists $c_1 \in \rz$ for which the Julia set of
$z --> z^L + c_1$ has positive Lebesgue measure.
This solves an old problem.
Editor's note: In 1997, it was shown by Xavier Buff that there
was a serious flaw in the argument, leaving a gap in the
proof. Currently (1999), the question of polynomials with
a positive measure Julia sets remains open.