Affiliation:
1. AGH University of Krakow, Faculty of Applied Mathematics , Mickiewicza 30 , , Poland
Abstract
Abstract
Let X be an Abelian group, Y be a commutative monoid, K ⊂Y be a submonoid and F : X → 2
Y
\ {∅} be a set-valued map. Under some additional assumptions on ideals ℐ
1 in X and ℐ
2 in X
2, we prove that if F is ℐ
2-almost everywhere K-additive, then there exists a unique up to K K-additive set-valued map G : X → 2
Y
\{∅} such that F = G ℐ
1-almost everywhere in X. Our considerations refers to the well known de Bruijn’s result [1].