On different types of non-additive set multifunctions

Abstract

Abstract: In this paper, we study different types of non-additive set multifunctions (such as: uniformly autocontinuous, null-additive, null-null-additive), presenting relationships among them and some of their properties regarding atoms and pseudo-atoms. We also study non-atomicity and non-pseudo-atomicity of regular null-additive set multifunctions defined on the Baire (Borel respectively) δ-ring of a Hausdorff locally compact space and taking values in the family of non-empty closed subsets of a real normed space. Key–words: uniformly autocontinuous, null-null-additive, (pseudo)-atom, non-(pseudo)-atomic, extension, regular, Darboux property.