  The pion structure function is investigated in a simple model, where the pion
and its constituent quark fields are coupled through the simplest pseudoscalar
coupling. The imaginary part of the forward gamma* pi -> gamma* pi scattering
amplitude is evaluated and related to the structure functions. It is shown that
the introduction of non-perturbative effects, linked to the size of the pion,
allows a connection with the quark distribution. It is predicted that
higher-twist terms become negligible for Q^2 larger than ~2 GeV^2, that quarks
in the pion have a momentum fraction smaller than in the proton case, and that
the momentum sum rule is violated for the pion.
