Abstract
For a metric space \((\mathbb {X},d)\) the classical Monge-Kantorovich metric d M gives a distance between two probability measures on \(\mathbb {X}\) which is tied to the underlying distance d on \(\mathbb {X}\) in an essential way. In this paper, we extend the Monge-Kantorovich metric to signed measures and set-valued measures (multimeasures) and, in each case, prove completeness of a suitable space of these measures. Using this extension as a framework, we construct self-similar multimeasures by using an IFS-type Markov operator.
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La Torre, D., Mendivil, F. The Monge–Kantorovich Metric on Multimeasures and Self–Similar Multimeasures. Set-Valued Var. Anal 23, 319–331 (2015). https://doi.org/10.1007/s11228-014-0310-7
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DOI: https://doi.org/10.1007/s11228-014-0310-7