On the weak-hash metric for boundedly finite integer-valued measures
arXiv:1803.02241 · doi:10.1017/S0004972718000485
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.
Minor typos corrected, Bulletin of the Australian Mathematical Society, 2018