Topology and convergence on the space of measure-valued functions

Takahiro Hasebe; Ikkei Hotta; Takuya Murayama

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arXiv · 2301.04361

Topology and convergence on the space of measure-valued functions

Takahiro Hasebe·Ikkei Hotta·Takuya Murayama

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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).

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Takahiro Hasebe, Ikkei Hotta, Takuya Murayama. 2023-01-11. Topology and convergence on the space of measure-valued functions. https://arxiv.org/abs/2301.04361

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