Smooth measures and positive continuous additive functionals attached to a compact nest
Probability
2025-09-30 v1
Abstract
The relationship between smooth measures and positive continuous additive functionals is well known, and this correspondence is called the Revuz correspondence. We investigate the relationships between several types of convergence of smooth measures and convergence of positive continuous additive functionals, mainly focusing on a treatment of nests. We provide conditions under which convergence of additive functionals implies convergence of the corresponding smooth measures. Our results cover convergence of smooth measures that are not Radon, including nowhere Radon measures.
Keywords
Cite
@article{arxiv.2509.23060,
title = {Smooth measures and positive continuous additive functionals attached to a compact nest},
author = {Takumu Ooi and Kaneharu Tsuchida and Toshihiro Uemura},
journal= {arXiv preprint arXiv:2509.23060},
year = {2025}
}
Comments
31 pages