  The lowest order radiative corrections to the cross section and asymmetries
measured in experiments on semi-inclusive deep inelastic scattering of
polarized particles were calculated. Both exact and leading log expressions
were presented and discussed for the total correction that include the
contributions from the processes of (i) real photon emission with
semi-inclusive processes, (ii) loop diagrams, and (iii) real photon emission
with exclusive processes. Radiative corrections to the Sivers and Collins
asymmetries in $\pi^+$ electroproduction were studied numerically within the
kinematical conditions of modern experimental environments at Jefferson
Laboratory (JLab). The Wandzura-Wilczek approximation for the semi-inclusive
structure functions and MAID2007 parameterization for the six amplitudes of
exclusive processes were used in numeric analyses. The results show that (i)
radiative effects can generate a correction comparable to the size of Sivers
and Collins asymmetries at the Born level, (ii) there is good agreement between
the exact and leading-order corrections, (iii) external functions (that is,
other than the Sivers and Collins functions in the respective asymmetries) can
generate a contribution to the radiative correction up to 20\%, and (iv) there
exists a strong dependence of the radiative correction on the models for
semi-inclusive and exclusive structure functions.
