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arXiv · 1803.02241

On the weak-hash metric for boundedly finite integer-valued measures

Maxime Morariu-Patrichi
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Abstract

It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes itself a complete separable metric space when endowed with the weak-hash metric. It is also known that convergence under this topology can be characterised in a way that is similar to the weak convergence of totally finite measures. However, the original proofs of these two fundamental results assume that a certain term is monotonic, which is not the case as we give a counterexample. We manage to clarify these original proofs by addressing specifically the parts that rely on this assumption and finding alternative arguments.

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Maxime Morariu-Patrichi. 2018-10-13. On the weak-hash metric for boundedly finite integer-valued measures. https://doi.org/10.1017/s0004972718000485

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