  Predictions for the transverse single spin asymmetry (SSA), A_N, are given
for the inclusive processes l p(transv. pol.) --> h X and l p(transv. pol.) -->
jet + X, which could be measured in operating or future experiments. These
estimates are based on the Sivers distributions and the Collins fragmentation
functions which fit the azimuthal asymmetries measured in semi-inclusive deep
inelastic scattering (SIDIS) processes (l p(transv. pol.) --> l' h X). The
factorization in terms of transverse momentum dependent distribution and
fragmentation functions (TMD factorization) - which supplies the theoretical
framework in which SIDIS azimuthal asymmetries are analyzed - is assumed to
hold also for the l p --> h X inclusive process at large P_T. A measurement of
A_N would then provide a direct test of the validity of the TMD factorization
in this case and would have important consequences for the study and
understanding of SSAs in p p(transv. pol.) --> h X processes.
