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How regular can maxitive measures be?

Paul Poncet 1, 2 
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We examine domain-valued maxitive measures defined on the Borel subsets of a topological space. Several characterizations of regularity of maxitive measures are proved, depending on the structure of the topological space. Since every regular maxitive measure is completely maxitive, this yields sufficient conditions for the existence of a cardinal density. We also show that every outer-continuous maxitive measure can be decomposed as the supremum of a regular maxitive measure and a maxitive measure that vanishes on compact subsets under appropriate conditions.
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Submitted on : Thursday, December 26, 2013 - 11:55:39 AM
Last modification on : Wednesday, February 2, 2022 - 3:52:08 PM

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Paul Poncet. How regular can maxitive measures be?. Topology and its Applications, Elsevier, 2013, 160 (4), pp.606-619. ⟨10.1016/j.topol.2013.01.007⟩. ⟨hal-00922372⟩



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