\(K\)-subadditive and \(K\)-superadditive set-valued functions bounded on ``large'' sets
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.
scientific article; zbMATH DE number 7439035
scientific article