# The idempotent Radon--Nikodym theorem has a converse statement

2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR
Abstract : Idempotent integration is an analogue of the Lebesgue integration where $\sigma$-additive measures are replaced by $\sigma$-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis, large deviation theory, or extreme value theory. Existence of Radon--Nikodym derivatives, which turns out to be crucial in all of these applications, was proved by Sugeno and Murofushi. Here we show a converse statement to this idempotent version of the Radon--Nikodym theorem, i.e. we characterize the $\sigma$-maxitive measures that have the Radon--Nikodym property.
Type de document :
Article dans une revue
Information Sciences, Elsevier, 2014, pp.115-124. 〈10.1016/j.ins.2014.02.074〉
Domaine :

https://hal.inria.fr/hal-00922377
Contributeur : Paul Poncet <>
Soumis le : jeudi 26 décembre 2013 - 12:07:41
Dernière modification le : jeudi 11 janvier 2018 - 06:22:33

### Citation

Paul Poncet. The idempotent Radon--Nikodym theorem has a converse statement. Information Sciences, Elsevier, 2014, pp.115-124. 〈10.1016/j.ins.2014.02.074〉. 〈hal-00922377〉

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