Weak Convergence of Topological Measures

Abstract Topological measures and deficient topological are defined on open closed subsets of a space, generalize regular Borel measures, correspond to (nonlinear in general) functionals that linear singly generated subalgebras or cones functions. They lack subadditivity, many standard techniques measure theory functional analysis do not apply them. Nevertheless, we show classical results probability hold for measures. In particular, prove version Aleksandrov’s theorem equivalent definitions weak convergence We also Prokhorov’s which relates the existence weakly convergent subsequence any sequence family characteristics being uniformly bounded variation tight family. define Prokhorov Kantorovich–Rubenstein metrics either them implies (deficient) metric spaces. known about various dense nowhere The present paper constitutes necessary step further research its applications context corresponding nonlinear functionals.