  Double hard scattering in proton-proton collisions is described in terms of
double parton distributions. We derive bounds on these distributions that
follow from their interpretation as probability densities, taking into account
all possible spin correlations between two partons in an unpolarized proton.
These bounds constrain the size of the polarized distributions and can for
instance be used to set upper limits on the effects of spin correlations in
double hard scattering. We investigate the stability of the bounds under
leading-order DGLAP evolution to higher scales.
