Discussiones Mathematicae Differential Inclusions 16(1) (1996) 91-97
Institute of Mathematics, Technical University
Podgórna 50, 65-246 Zielona Góra, Poland
Let (T, F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rn) is said to be decomposable if for every A∈F and f∈K, g∈K one has fχA+gχT\A ∈ K. Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
Keywords: set-valued function, continuous selection, fixed point,decomposability, set-valued stochastic processes.
1991 Mathematics Subject Classification: 54C65, 54C60.
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