Proof of factorization for electroproduction of multiple mesons and exclusiveγ*γproduction of multiple hadrons

In the following, we will present a generalization of the proof of factorization for electroproduction of vector mesons to the production of several mesons such as ${\pi }^{+}{\pi }^{-}$ and a proof of factorization for exclusive ${\gamma }^{*}\gamma$ production of several hadrons, for example, $p\overline{p}$ or ${\pi }^{+}{\pi }^{-},$ to all orders in perturbation theory up to power suppressed terms.