  Double hard scattering can play an important role for producing multiparticle
final states in hadron-hadron collisions. The associated cross sections depend
on double parton distributions, which at present are only weakly constrained by
theory or measurements. A set of sum rules for these distributions has been
proposed by Gaunt and Stirling some time ago. We give a proof for these sum
rules at all orders in perturbation theory, including a detailed analysis of
the renormalisation of ultraviolet divergences. As a by-product of our study,
we obtain the form of the inhomogeneous evolution equation for double parton
distributions at arbitrary perturbative order.
