Explicit expressions and computational methods for the Fortet–Mourier distance of positive measures to finite weighted sums of Dirac measures

Journal of Approximation Theory, vol. 294, pp. 105947

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.

Authors 2

1. Sander C. Hille corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

2. Esmée S. Theewis

   Delft University of Technology

   Affiliation as printed

   Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands