On Almost Everywhere K-Additive Set-Valued Maps

Eliza Jabłońska

doi:10.2478/amsil-2023-0025

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On Almost Everywhere K-Additive Set-Valued Maps

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 1 (March 2024)

By: Eliza Jabłońska

Open Access

|Dec 2023

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].

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0025 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 29 - 36

Submitted on: Jun 27, 2023

Accepted on: Dec 5, 2023

Published on: Dec 13, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

monoid,

Abelian group,

-additive set-valued map,

ideal,

almost everywhere

Related subjects:

Mathematics,

General mathematics

© 2023 Eliza Jabłońska, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 1 (March 2024)