Topological spaces with the strong Skorokhod property (Q2761587)

The authors study topological spaces with the strong Skorokhod property, that is spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measures on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost surely convergent sequences of mappings. The paper considers nonmetrizable spaces with such a property. Especially, a new class of so called almost metrizable spaces is introduced and it is shown that such a space has the strong Skorokhod property if and only if it is sequentially Prokhorov. Some examples of nonmetrizable spaces with and without the strong Skorokhod property are given and a large number of open problems are posed.