Topology and convergence on the space of measure-valued functions
Probability
2026-01-13 v3
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 L\'evy'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).
Keywords
Cite
@article{arxiv.2301.04361,
title = {Topology and convergence on the space of measure-valued functions},
author = {Takahiro Hasebe and Ikkei Hotta and Takuya Murayama},
journal= {arXiv preprint arXiv:2301.04361},
year = {2026}
}
Comments
(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)