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  • ON THE WEAK-HASH METRIC FOR BOUNDEDLY FINITE INTEGER-VALUED MEASURES

  • Part of
  • MAXIME MORARIU-PATRICHI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 98 / Issue 2 / October 2018
    Published online by Cambridge University Press:
    19 July 2018, pp. 265-276
    Print publication:
    October 2018
    • Article
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  • It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes 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 show by a counterexample. We clarify these original proofs by addressing the parts that rely on this assumption and finding alternative arguments.