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On studying bi-\(\Gamma\)-algebra and some related concepts | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 128، دوره 13، شماره 1، خرداد 2022، صفحه 1565-1572 اصل مقاله (360.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5772 | ||
| نویسندگان | ||
| Mohaimen M. Abbood* 1؛ Ali Al-Fayadh Ali Al-Fayadh2؛ Hassan H. Ebrahim3 | ||
| 1Ministry of Education, General Directorate of Education in Diyala, Iraq | ||
| 2Department of Mathematics and Computer Applications, College of Science, Al-Nahraini University, Baghdad, Iraq | ||
| 3Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq | ||
| تاریخ دریافت: 13 شهریور 1400، تاریخ پذیرش: 08 آبان 1400 | ||
| چکیده | ||
| The aim of this research paper is to introduce the concept of bi-\(\Gamma\)-algebra space (bi-gamma algebra space). The concept of bi-\(\mu\)-measurable set in a bi-\(\Gamma\)-algebra space is defined. With this concept, some properties of bi-\(\Gamma\)-algebra space are proved. We then define various separation axioms for bi-\(\Gamma\)-algebra space such as \(M_{0},M_{1},\ M_{2},\ M_{3},\) and \(M_{4}\); then the relationships between them are studied. In addition, the concept of measurable function between two bi-measurable spaces is introduced and some results are discussed. | ||
| کلیدواژه‌ها | ||
| algebra؛ ( \sigma)-field؛ (\sigma)-algebra؛ (\Gamma)-algebra؛ measurable function | ||
| مراجع | ||
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[1] M.M. Abbood, H.H. Ebrahim and A. Al-Fayadh, Study on Γ–algebra with some related concepts, Accepted to AIP Conf. Proc., 28/3/2021. [2] V.I. Bogachev, Measure Theory I, Springer, 2007. [3] R.M. Dudley, Real analysis and probability, Cambridge Univ. Press, 2002. [4] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties, CRC Press. New York, 2015. [5] P.R. Halmos, Measure Theory, Springer, 1976. [6] B.A. Robert, Real Analysis and Probability, Academic Press, INC, University of Illinois, 1972. [7] K. A. Ross and R. B. Ash, Real analysis and probability, Amer. Math. Month. 82(1) (1975) 91. [8] Z. Wang and G. J. Klir, Generalized measure theory, Foundations, 25 (2008).[1] M.M. Abbood, H.H. Ebrahim and A. Al Fayadh, Study on Γ–algebra with some related concepts, Accepted to AIP Conf. Proc., 28/3/2021. | ||
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