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A function s: K n → R n , defined on the family K n of all compact convex and nonempty sets in R n , is called a Minkowski additive selection, provided s(A + B) = s(A) + s(B) and s(A) ∈ A, whenever A, B ∈ K n . We confirm the conjecture [6] that there exist extremal selections which are not regular (s is regular if s(A) ∈ ext A, A ∈ K n )

Nonregular extreme points in the set of Minkowski additive selections