Mosco convergence

Summary

Mosco convergence is a convergence of functionals on a normed space that combines the weak and the strong topology. It asks for the lower bound inequality of Γ-convergence along weakly convergent sequences and for recovery sequences that converge strongly. It was introduced by Umberto Mosco to study the stability of variational inequalities when the constraint sets change. In finite dimension it is the same as Γ-convergence; in general it implies Γ-convergence for both the weak and the norm topology. The definition gives the precise conditions.