A Lyapunov-Type Theorem for Nonadditive Vector Measures

  • Nobusumi Sagara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5861)


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.


Nonatomic vector measure Lyapunov’s convexity theorem Capacity Supermodularity Choquet integral Convex game Core Fair division 

MSC 2000

Primary: 28B05 28E10 secondary: 91A12 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nobusumi Sagara
    • 1
  1. 1.Faculty of EconomicsHosei UniversityTokyoJapan

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