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Subadditive set-valued functions. (English) Zbl 0617.26010
A set-valued function $$F:[0,\infty)\to 2^ Y$$, where Y is a normed space, is said to be subadditive if $$F(s+t)\subset F(s)+F(t)$$ for all $$s,t\in [0,\infty)$$. The author proves that if a subadditive function F with compact, convex and non-empty values is measurable, then there exists a non-empty set A such that $$tA\subset F(t)$$, $$t\in [0,\infty)$$.
Reviewer: K.Nikodem

##### MSC:
 26E25 Set-valued functions 39B72 Systems of functional equations and inequalities