A functional representation of the capacity multiplication monad

Taras Radul


Functional representations of the capacity monad based on the max and min operations were considered in [10] and [7]. Nykyforchyn considered in [8] some alternative monad structure for the possibility capacity functor based on the max and usual multiplication operations. We show that such a capacity monad (which we call the capacity multiplication monad) has a functional representation, i.e. the space of capacities on a compactum X can be naturally embedded (with preservation of the monad structure) in some space of functionals on CX,I. We also describe this space of functionals  in terms of properties of functionals.

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DOI: http://dx.doi.org/10.30970/vmm.2018.86.125-133


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