  We formulate the momentum-space Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
(DGLAP) evolution equations for structure functions measurable in deeply
inelastic scattering. We construct a six-dimensional basis of structure
functions that allows for a full three flavor structure and thereby provides a
way to calculate perturbative predictions for physical cross sections directly
without unobservable parton distribution functions (PDFs) and without the
associated scheme dependence. We derive the DGLAP equations to first non-zero
order in strong coupling $\alpha_s$, but the approach can be pursued to
arbitrary order in perturbation theory. We also numerically check our equations
against the conventional PDF formulation.
