# Continuity of argmin

Where here we ask what happens to the infima and sets of minimisers of sequences of functions ? under what conditions do these converge? what is an appropriate notion of convergence for functions which transfers the convergence to the corresponding sequence of its minima and minimizers? This poses a question of *continuity* for the infimum (as an operator) as well as the set of minimisers (as a multi-valued operator). We aim at characterising the continuity of these operators. Continue reading →