Approximation of capacities with additive measures

  • O.R. Nykyforchyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine; Casimir the Great University in Bydgoszcz, 30 J.K. Chodkiewicza str., 85064, Bydgoszcz, Poland
  • I.D. Hlushak Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
https://doi.org/10.15330/cmp.9.1.92-97
Keywords: Prokhorov metric, non-additive measure, approximation, compact metric space
Published online: 2017-06-23

Abstract


For a space of non-additive regular measures on a metric compactum with the Prokhorov-style metric, it is shown that the problem of approximation of arbitrary measure with an additive measure on a fixed finite subspace reduces to linear optimization problem with parameters dependent on the values of the measure on a finite number of sets.

An algorithm for such an approximation, which is more efficient than the straighforward usage of simplex method, is presented.

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How to Cite
(1)
Nykyforchyn O., Hlushak I. Approximation of Capacities With Additive Measures. Carpathian Math. Publ. 2017, 9 (1), 92-97.