  We show that the gravitational magnification factor averaged over all
configurations of lenses in a locally inhomogeneous universe satisfy a second
order differential equation with redshift $z$ by taking the continuous limit of
multi-plane gravitational lens equation (the number $N$ of lenses $\to\infty$)
and that the gravitationally magnified Dyer-Roeder distance in a clumpy
universe becomes to that of the Friedmann-Lema\^{\i}tre universe for arbitrary
values of the density parameter $\Omega_{0}$ and of a mass fraction
$\bar{\alpha}$ (smoothness parameter).
