Topology and convergence on the space of measure-valued functions

Abstract

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including Lévy's continuity theorem and functional limit theorems for (classical and non-commutative) additive processes, are also described. N.B.: the contents of this manuscript have been incorporated into another manuscript (arXiv:2412.18742).

(v1) 20 pages. (v2) 11 pages. The title has been changed. (v3) 11 pages. As written in the abstract, the contents of this manuscript have been incorporated into another manuscript (arXiv:2412.18742)