  We examine the relation of moments of parton distribution functions to matrix
elements of non-local operators computed in lattice quantum chromodynamics. We
argue that after the continuum limit is taken, these non-local matrix elements
give access to moments that are finite and can be matched to those defined in
the $\overline{MS}$ scheme. We demonstrate this fact with a numerical
computation of moments through non-local matrix elements in the quenched
approximation and we find that these moments are in excellent agreement with
the moments obtained from direct computations of local twist-2 matrix elements
in the quenched approximation.
