In this paper we study properties of the Aumann integral of set-valued functions F defined on a σ-finite nonatomic measure space (T,Σ,μ) and with values in a real separable reflexive Banach space. Among others, we establish a representation theorem under the assumption that Σ has the Suslin operation and F is of Suslin type or that Σ is μ-complete and the values of F are closed sets. In particular, we also extend earlier results of R. J. Aumann [same journal 12 (1965), 1-12], Z. Artstein [Indiana Univ. Math. J. 24 (1974/75), 433-441] and R. Datko [Fund. Math. 78 (1973), 205-208].
A representation theorem for Aumann integrals
PUCCI, Patrizia;
1984
Abstract
In this paper we study properties of the Aumann integral of set-valued functions F defined on a σ-finite nonatomic measure space (T,Σ,μ) and with values in a real separable reflexive Banach space. Among others, we establish a representation theorem under the assumption that Σ has the Suslin operation and F is of Suslin type or that Σ is μ-complete and the values of F are closed sets. In particular, we also extend earlier results of R. J. Aumann [same journal 12 (1965), 1-12], Z. Artstein [Indiana Univ. Math. J. 24 (1974/75), 433-441] and R. Datko [Fund. Math. 78 (1973), 205-208].File in questo prodotto:
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