Since lower and upper bound inequalities of this type are used in the definition of Γ-convergence, Mosco convergence is sometimes phrased as “weak Γ-liminf and strong Γ-limsup” convergence.
Since these specific types of lower and upper bound inequalities are essential in the definition of Γ-convergence, Mosco convergence can be described as “weak Γ-liminf and strong Γ-limsup” convergence.