and $\nu$ is a random regular measure forcing $u$ to stay above $S$ and satisfying a minimal Skohorod condition.\
In order to give a rigorous meaning to the notion of solution, inspired by the works of M. Pierre in the deterministic case (see [@Pierre; @PIERRE]), we introduce the notion of parabolic capacity. The key point is that in [@DMZ12], we construct a solution which admits a quasi continuous version hence defined outside a polar set and that regular measures which in general are not absolutely continuous w.r.t. the Lebesgue measure, do not charge polar sets.\
There is a huge literature on parabolic SPDE’s without obstacle. The study of the $L^p-$norms w.r.t. the randomness of the space-time uniform norm on the trajectories of a stochastic PDE was started by N. V. Krylov in [@Krylov], for a more complete overview of existing works on this subject see [@DMS09; @DM11] and the references therein. Concerning the obstacle problem, there are two approaches, a probabilistic one (see [@MatoussiStoica; @Klimsiak]) based on the Feynmann-Kac’s formula via the backward doubly stochastic differential equations and the analytical one (see [@DonatiPardoux; @NualartPardoux; @XuZhang]) based on the Green function.\
To our knowledge, up to now there is no maximum 