  In this note we reexamine the possibility of extracting parton distribution
functions from lattice simulations. We discuss the case of quasi-parton
distribution functions, the possibility of using the reduced Ioffe-time
distributions and the more recent proposal of directly making reference to the
computation of the current-current $T$-product. We show that in all cases the
process of renormalization hindered by lattice momenta limitation represents an
obstruction to a direct Euclidean calculation of the parton distribution
function.
