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

Part of: Classical measure theory Stochastic processes

Published online by Cambridge University Press:  19 July 2018

MAXIME MORARIU-PATRICHI Open the ORCID record for MAXIME MORARIU-PATRICHI [Opens in a new window]
MAXIME MORARIU-PATRICHI*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK email [email protected]
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Abstract

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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.

Keywords

boundedly finite integer-valued measuresweak-hash metriccompletenessseparabilityBorel sigma-algebra characterisationconvergence characterisation

MSC classification

Primary: 28A33: Spaces of measures, convergence of measures
Secondary: 60G55: Point processes
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 2 , October 2018 , pp. 265 - 276
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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