  In games with continuous strategy spaces, if a rest point of the replicator
dynamics is asymptotically stable then the rest point must be finitely
supported (van Veelen, M., Spreij, P., 2009. Evolution in games with a
continuous action space. Econom. Theory 39 (3), 355-376). In this article, we
address the converse question that is, we prove that a finitely supported
population state is asymptotically stable with respect to the variational norm
when it is strongly uninvadable.
