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The aim of this paper is to investigate extremum problems with pay-off the total variational distance metric subject to linear functional constraints both defined on the space of probability measures, as well as related problems. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstractdoi:10.1109/cdc.2013.6760046 dblp:conf/cdc/CharalambousTLC13 fatcat:wu5753q6kje4ho7tfdjsf5ddsu