Random theorems in topology
Regularization of closed-valued multifunctions in a non-metric setting
Relaxation theorem for set-valued functions with decomposable values
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 . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.