  In the paper, we consider the obstacle problem, with one and two irregular
barriers, for semilinear evolution equation involving measure data and operator
corresponding to a semi-Dirichlet form. We prove the existence and uniqueness
of solutions under the assumption that the right-hand side of the equation is
monotone and satisfies mild integrability conditions. To treat the case of
irregular barriers, we extend the theory of precise versions of functions
introduced by M. Pierre. We also give some applications to the so-called
switching problem.
