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  "body": "\n## Summary\n\nMosco convergence is a convergence of functionals on a normed space that combines the weak and the strong topology.\nIt asks for the lower bound inequality of [[Γ-convergence|NW9MM370A5]] along weakly convergent sequences and for recovery sequences that converge strongly.\nIt was introduced by Umberto Mosco to study the stability of variational inequalities when the constraint sets change.\nIn finite dimension it is the same as Γ-convergence; in general it implies Γ-convergence for both the weak and the norm topology.\nThe [[definition|RNDKD74V17]] gives the precise conditions.\n\n## Explanations\n\n### L1 human\n\nIn an infinite-dimensional space, bounded sequences often have no strongly convergent subsequence, but they have weakly convergent ones.\nSo a useful lower bound must hold along weakly convergent sequences, while a useful approximation should be as good as possible, that is strong.\nMosco convergence asks for exactly this pair of conditions.\nFor closed convex sets $K_n$ it says two things.\nWeak limits of points of $K_n$ lie in the limit set $K$, and each point of $K$ is a strong limit of points of $K_n$.\nFor example, the segments $K_n = [0, 1 - 1/n]$ in $\\R$ converge in this sense to $[0, 1]$.\n",
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