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The paper is devoted to the description of extreme points in the set of 2-monotone measures. We describe them using lattices on which an extreme 2-monotone measure is additive. We also propose the way of generation extreme monotone measures based on the aggregation of extreme measures with the help of multilinear extension. We describe also the class of extreme 2-monotone measures that are additive on the filter on which a 2-monotone measure has a positive values.
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