%0 Journal Article
%T On studying bi-\(\Gamma\)-algebra and some related concepts
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Abbood, Mohaimen M.
%A Ali Al-Fayadh, Ali Al-Fayadh
%A Ebrahim, Hassan H.
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 1565-1572
%! On studying bi-\(\Gamma\)-algebra and some related concepts
%K algebra
%K ( sigma)-field
%K (sigma)-algebra
%K (Gamma)-algebra
%K measurable function
%R 10.22075/ijnaa.2022.5772
%X 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.
%U https://ijnaa.semnan.ac.ir/article_5772_cb31ac7125b59a219f98eccaffbe1dd0.pdf