more suitable unless in some special cases. However, it also seems that even the nonsequential Fatou property is … that ρ satisfies the nonsequential Fatou property if liminf i ρ(Xi) ≥ρ(X) holds whenever (Xi)i∈I is a uniformly bounded net … limit of a sequence in Ar. Lemma 2.1 Under (2.1) ρ satisfies the nonsequential Fatou property if and only if it fulfills the …