On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring
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 o...
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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2022-10-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5771 |
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| author | Samah H. Asaad Ibrahim S. Ahmed Hassan H. Ebrahim |
| author_facet | Samah H. Asaad Ibrahim S. Ahmed Hassan H. Ebrahim |
| author_sort | Samah H. Asaad |
| collection | DOAJ |
| description |
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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| format | Article |
| id | doaj-art-71cdf03673ca4ba9bfd59c5482dbd2c4 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2022-10-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-71cdf03673ca4ba9bfd59c5482dbd2c42025-08-20T03:34:01ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862022-10-0119510.21123/bsj.2022.5771On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ringSamah H. Asaad0Ibrahim S. Ahmed1Hassan H. Ebrahim2Department of Physics, College of Education-Tuzkhurmatu, Tikrit University, Salahaddin, Iraq.Department of Physics, College of Education-Tuzkhurmatu, Tikrit University, Salahaddin, IraqDepartment of Mathematics, College of Computer Science and Mathematics, Tikrit University, Salahaddin, Iraq 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. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5771Countably weakly null-additive, Measure, Null-additive, σ–field, σ–ring |
| spellingShingle | Samah H. Asaad Ibrahim S. Ahmed Hassan H. Ebrahim On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring مجلة بغداد للعلوم Countably weakly null-additive, Measure, Null-additive, σ–field, σ–ring |
| title | On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring |
| title_full | On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring |
| title_fullStr | On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring |
| title_full_unstemmed | On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring |
| title_short | On Finitely Null-additive and Finitely Weakly Null-additive Relative to the σ–ring |
| title_sort | on finitely null additive and finitely weakly null additive relative to the σ ring |
| topic | Countably weakly null-additive, Measure, Null-additive, σ–field, σ–ring |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5771 |
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