On almost everywhere K-additive set-valued maps

Eliza Jabłońska

Published: 2023-12-13

Vol. 38 No. 1 (2024)

On almost everywhere K-additive set-valued maps

Eliza Jabłońska

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 ℐ₁in X and ℐ₂in X², 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 ℐ₁-almost everywhere in X. Our considerations refers to the well known de Bruijn’s result [1].

Keywords:

monoid , Abelian group , K-additive set-valued map , ideal , almost everywhere

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Jabłońska, E. (2023). On almost everywhere K-additive set-valued maps. Annales Mathematicae Silesianae, 38(1), 29–36. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/16500

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Vol. 38 No. 1 (2024)
Published: 2024-03-27

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

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