  We generalize various notions of stability of invariant sets of dynamical
systems to invariant measures, by defining a topology on the set of measures.
The defined topology is similar, but not topologically equivalent to weak*
topology, and it also differs from topologies induced by the Riesz
Representation Theorem. It turns out that the constructed topology is a
solution of a limit case of a $p$-optimal transport problem, for $p=\infty$.
