On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring

• DOI: 10.21123/bsj.2022.5771
• Publication Date: 2022-03-19T18:54:27Z
• Authors: Samah H. Asaad; Ibrahim S. Ahmed; Hassan H. Ebrahim
• Keywords: Science; Q; 0103 physical sciences; Countably weakly null-additive, Measure, Null-additive, σ–field, σ–ring; 01 natural sciences

This article introduces the concept of finitely null-additive set function relative to the σ– ring and many properties of this concept have been discussed. Furthermore, to introduce and study the notion of finitely weakly null-additive set function relative to the σ– ring as a generalization of some concepts such as measure, countably additive, finitely additive, countably null-additive, countably weakly null-additive and finitely null-additive. As the first result, it has been proved that every finitely null-additive is a finitely weakly null-additive. Finally, the paper introduces a study of the concept of outer measure as a stronger form of finitely weakly null-additive.