  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 $\mathcal{P}$ is a (possibly non-dominated) class of
probability measures. Applications of our results lie within robust versions
the Fundamental Theorem of Asset Pricing or dual representation of convex risk
measures.
