Abstract
Given a capacityc and a probability measurep on a finite set, there is a natural way to combinec andp to produce a measure. For fixedc, these measures are probability measures for allp precisely whenc is monotone, and dominatec for allp precisely whenc is 2-monotone.
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Sundberg, C., Wagner, C. Characterizations of monotone and 2-monotone capacities. J Theor Probab 5, 159–167 (1992). https://doi.org/10.1007/BF01046783
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DOI: https://doi.org/10.1007/BF01046783