On a convergence of positive continuous additive functionals in terms of their smooth measures

Yasuhito Nishimori; Matsuyo Tomisaki; Kaneharu Tsuchida; Toshihiro Uemura

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arXiv · 2405.03937

On a convergence of positive continuous additive functionals in terms of their smooth measures

Yasuhito Nishimori·Matsuyo Tomisaki·Kaneharu Tsuchida·Toshihiro Uemura

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Abstract

A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric on the space of measures of finite energy integrals and show some structures of the metric. Then, we show the compactness and give some examples of positive continuous additive functionals that the convergence holds in terms of the associated smooth measures.

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Yasuhito Nishimori, Matsuyo Tomisaki, Kaneharu Tsuchida, Toshihiro Uemura. 2024-05-07. On a convergence of positive continuous additive functionals in terms of their smooth measures. https://arxiv.org/abs/2405.03937

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