Before revision: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of   -quasisure bounded random variables, where   is a (possibly non-dominated) class of probability measures.
After revision: We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of  \mathcal{P -quasisure bounded random variables, where  is a (possibly non-dominated) class of probability measures.