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Mathematics > Functional Analysis

arXiv:2206.12234 (math)
[Submitted on 24 Jun 2022 (v1), last revised 8 Jul 2022 (this version, v2)]

Title:Explicit expressions and computational methods for the Fortet-Mourier distance to finite weighted sums of Dirac measures

Authors:Sander C. Hille, Esmée S. Theewis
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Abstract:Explicit expressions and computational approaches are given for the Fortet-Mourier distance between a positively weighted sum of Dirac measures on a metric space and a positive finite Borel measure. Explicit expressions are given for the distance to a single Dirac measure. For the case of a sum of several Dirac measures one needs to resort to a computational approach. In particular, two algorithms are given to compute the Fortet-Mourier norm of a molecular measure, i.e. a finite weighted sum of Dirac measures. It is discussed how one of these can be modified to allow computation of the dual bounded Lipschitz (or Dudley) norm of such measures.
Subjects: Functional Analysis (math.FA)
Cite as: arXiv:2206.12234 [math.FA]
  (or arXiv:2206.12234v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.2206.12234

Submission history

From: Sander Hille [view email]
[v1] Fri, 24 Jun 2022 12:04:07 UTC (17 KB)
[v2] Fri, 8 Jul 2022 09:20:26 UTC (631 KB)
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