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