  We prove a Skoda-type division theorem via a degeneration argument. The proof
is inspired by B. Berndtsson and L. Lempert's approach to the $L^2$ extension
theorem and is based on positivity of direct image bundles. The same tools are
then used to slightly simplify and extend the proof of the $L^2$ extension
theorem given by Berndtsson and Lempert.
