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

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Samah H. Asaad
https://orcid.org/0000-0002-5098-2124
Ibrahim S. Ahmed
https://orcid.org/0000-0003-4466-3263
Hassan H. Ebrahim
https://orcid.org/0000-0001-6931-9392

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.

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Asaad SH, Ahmed IS, Ebrahim HH. On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring. Baghdad Sci.J [Internet]. 2022 Oct. 1 [cited 2022 Nov. 30];19(5):1148. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5771
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