Smooth measures and positive continuous additive functionals attached to a compact nest

Takumu Ooi; Kaneharu Tsuchida; Toshihiro Uemura

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arXiv · 2509.23060

Smooth measures and positive continuous additive functionals attached to a compact nest

Takumu Ooi·Kaneharu Tsuchida·Toshihiro Uemura

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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.

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Takumu Ooi, Kaneharu Tsuchida, Toshihiro Uemura. 2025-09-27. Smooth measures and positive continuous additive functionals attached to a compact nest. https://arxiv.org/abs/2509.23060

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