A Lyapunov-Type Theorem for Nonadditive Vector Measures
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We prove the convexity and compactness of the closure of the lower partition range of an ℝ n -valued, nonatomic, supermodular capacity, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to fair division problems, and the existence of Pareto optimal α-fair partitions is demonstrated for the case of nonadditive measures.
KeywordsNonatomic vector measure Lyapunov’s convexity theorem Capacity Supermodularity Choquet integral Convex game Core Fair division
MSC 2000Primary: 28B05 28E10 secondary: 91A12
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