Concave measures and the fuzzy core of exchange economies with heterogeneous divisible commodities

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of individuals are given by nonadditive utility functions defined on a σ-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many individuals. Applying the Yosida–Hewitt decomposition theorem, we also demonstrate that partitions in the fuzzy core are supportable by prices in L1.