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

Authors

Samah H. Asaad, Department of Physics, College of Education-Tuzkhurmatu, Tikrit University, Salahaddin, Iraq.Follow
Ibrahim S. Ahmed, Department of Physics, College of Education-Tuzkhurmatu, Tikrit University, Salahaddin, IraqFollow
Hassan H. Ebrahim, Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Salahaddin, IraqFollow

Abstract

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.

Keywords

Countably weakly null-additive, Measure, Null-additive, σ–field, σ–ring

Article Type

Article

How to Cite this Article

Asaad, Samah H.; Ahmed, Ibrahim S.; and Ebrahim, Hassan H. (2022) "On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring," Baghdad Science Journal: Vol. 19: Iss. 5, Article 3.
DOI: https://doi.org/10.21123/bsj.2022.5771