Smooth measures and positive continuous additive functionals attached to a compact nest
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909812477919232 |
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| author | Ooi, Takumu Tsuchida, Kaneharu Uemura, Toshihiro |
| author_facet | Ooi, Takumu Tsuchida, Kaneharu Uemura, Toshihiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth measures and positive continuous additive functionals attached to a compact nest Ooi, Takumu Tsuchida, Kaneharu Uemura, Toshihiro Probability 31C25, 60J55, 28A33 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. |
| title | Smooth measures and positive continuous additive functionals attached to a compact nest |
| topic | Probability 31C25, 60J55, 28A33 |
| url | https://arxiv.org/abs/2509.23060 |