Graphical convergence of sums of monotone mappings

Abstract

Abstract. This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finitedimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of convex functions is given. Counterexamples are used to show that the results cannot be directly extended to infinite dimensions.

Tails of optimal transport plans for regularly varying probability measures

“…As gph(∂ ψ) is the Painlevé-Kuratowski limit of gph(∂ψ n ) as n → ∞ in M , it is also equal to the inner limit of those sets, which contains the inner limit of gph(∂ψ n ) as n → ∞ in the larger subsequence N . By (18), we find spt(π) ⊂ gph(∂ ψ). (b) Let (π, ∂ ψ) be a possible subsequence limit in (a).…”