Mosco convergence
In mathematical analysis, Mosco convergence is a notion of convergence for functionals that is used in nonlinear analysis and set-valued analysis. It is a particular case of Γ-convergence. Mosco convergence is sometimes phrased as “weak Γ-liminf and strong Γ-limsup” convergence since it uses both the weak and strong topologies on a topological vector space "X". In finite dimensional spaces, Mosco convergence coincides with epi-convergence. "Mosco convergence" is named after Italian mathematician Umberto Mosco, a current Harold J. Gay professor of mathematics at Worcester Polytechnic Institute. Definition. Let "X" be a topological vector space  and let "X" denote the dual space of continuous linear functionals on "X". Let "F" : "X" → [0, +∞] be functionals on "X" for each "n" = 1, 2, ... The sequence (or, more generally, net) ("F") is said to Mosco converge to another functional "F" : "X" → [0, +∞] if the following two conditions hold: 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. Mosco convergence is sometimes abbreviated to M-convergence and denoted by Mosco