Convexity and Closure in Optimal Allocations Determined by Decomposable Measures

  • Zvi ArtsteinEmail author


A general optimal allocation problem is considered, where the decision-maker controls the distribution of acting agents, by choosing a probability measure on the space of agents. The notion of a decomposable family of probability measures is introduced, in the spirit of a decomposable family of functions. It provides a sufficient condition for the convexity of the feasible set, and the concavity of the value function. Together with additional conditions, closure properties also follow. The notion of a decomposable family of measures covers, both the case of set-valued integrals and the case of convexity in the space of probability measures.


Optimal allocations Decomposable family of measures Convexity of feasible set 

Mathematics Subject Classification (2010)

Primary 91B32 Secondary 28B20 



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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.The Weizmann Institute of ScienceRehovotIsrael

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