For a metric space (X,d) the classical Monge-Kantorovich metric dM gives a distance between two probability measures on X which is tied to the underlying distance don 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.

The Monge–Kantorovich metric on multimeasures and self–similar multimeasures / D. La Torre, F. Mendivil. - In: SET-VALUED AND VARIATIONAL ANALYSIS. - ISSN 1877-0533. - 23:2(2015 Jun), pp. 319-331.

The Monge–Kantorovich metric on multimeasures and self–similar multimeasures

D. La Torre
Primo
;
2015

Abstract

For a metric space (X,d) the classical Monge-Kantorovich metric dM gives a distance between two probability measures on X which is tied to the underlying distance don 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.
Monge-Kantorovich metric; Set-valued measures; Spaces of measures; Iterated function systems; Zonotope
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/251293
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