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Journal Articles Information Sciences Year : 2014

The idempotent Radon--Nikodym theorem has a converse statement

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.

Dates and versions

hal-00922377 , version 1 (26-12-2013)

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Paul Poncet. The idempotent Radon--Nikodym theorem has a converse statement. Information Sciences, 2014, 271, pp.115-124. ⟨10.1016/j.ins.2014.02.074⟩. ⟨hal-00922377⟩
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