\(K\)-subadditive and \(K\)-superadditive set-valued functions bounded on ``large'' sets
type: Item
instance of: scholarly article
title: \(K\)-subadditive and \(K\)-superadditive set-valued functions bounded on ``large'' sets
zbMATH Open document ID: 1482.39038
author: Eliza Jabłońska
author: Kazimierz Nikodem
published in: Aequationes Mathematicae
publication date: 2021-12-06T00:00:00Z
review text: The authors study the concepts of \(K\)-subadditive and \(K\)-superadditive set-valued functions bounded on ``large'' sets. In particular, it is proved that every \(K\)-subadditive set-valued map is weakly \(K\)-upper bounded on a ``large'' set (e.g., not null-finite, not Haar-null or not a Haar-meager set). Furthermore, it is proved that any \(K\)-superadditive set-valued map is \(K\)-lower bounded on a ``large'' set, is locally \(K\)-lower bounded and locally weakly \(K\)-upper bounded at every point of its domain. Examples are provided to support some of the obtained results.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 7439035
zbMATH Keywords: \(K\)-subadditive function
zbMATH Keywords: \(K\)-superadditive function
zbMATH Keywords: set-valued map
zbMATH Keywords: null-finite set
zbMATH Keywords: Haar-null set
zbMATH Keywords: Haar-meager set
MaRDI profile type: Publication
full work available at URL: s00010-021-00850-6
OpenAlex ID: W3206924291
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DOI: 10.1007/S00010-021-00850-6
description: scientific article; zbMATH DE number 7439035