  We study parabolic operators H = $\partial$t -- div $\lambda$,x A(x,
t)$\nabla$ $\lambda$,x in the parabolic upper half space R n+2 + = {($\lambda$,
x, t) : $\lambda$ > 0}. We assume that the coefficients are real, bounded,
measurable, uniformly elliptic, but not necessarily symmetric. We prove that
the associated parabolic measure is absolutely continuous with respect to the
surface measure on R n+1 in the sense defined by A$\infty$(dx dt). Our argument
also gives a simplified proof of the corresponding result for elliptic measure.
